TSTP Solution File: SET700+4 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SET700+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 03:04:22 EDT 2022
% Result : Theorem 8.97s 9.26s
% Output : CNFRefutation 9.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 30
% Syntax : Number of formulae : 556 ( 355 unt; 18 typ; 0 def)
% Number of atoms : 3092 ( 875 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 6485 (1207 ~; 979 |; 72 &;4186 @)
% ( 27 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 6 con; 0-2 aty)
% Number of variables : 1611 ( 0 ^1609 !; 2 ?;1611 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_difference,type,
difference: $i > $i > $i ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_equal_set,type,
equal_set: $i > $i > $o ).
thf(tp_intersection,type,
intersection: $i > $i > $i ).
thf(tp_member,type,
member: $i > $i > $o ).
thf(tp_power_set,type,
power_set: $i > $i ).
thf(tp_product,type,
product: $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY31,type,
sK2_SY31: $i ).
thf(tp_sK3_SY33,type,
sK3_SY33: $i ).
thf(tp_sK4_Y,type,
sK4_Y: $i > $i > $i ).
thf(tp_sK5_Y,type,
sK5_Y: $i > $i > $i ).
thf(tp_sK6_X,type,
sK6_X: $i > $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_sum,type,
sum: $i > $i ).
thf(tp_union,type,
union: $i > $i > $i ).
thf(tp_unordered_pair,type,
unordered_pair: $i > $i > $i ).
thf(1,axiom,
! [X: $i,A: $i] :
( ( member @ X @ ( product @ A ) )
<=> ! [Y: $i] :
( ( member @ Y @ A )
=> ( member @ X @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product) ).
thf(2,axiom,
! [X: $i,A: $i] :
( ( member @ X @ ( sum @ A ) )
<=> ? [Y: $i] :
( ( member @ Y @ A )
& ( member @ X @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum) ).
thf(3,axiom,
! [X: $i,A: $i,B: $i] :
( ( member @ X @ ( unordered_pair @ A @ B ) )
<=> ( ( X = A )
| ( X = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair) ).
thf(4,axiom,
! [X: $i,A: $i] :
( ( member @ X @ ( singleton @ A ) )
<=> ( X = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton) ).
thf(5,axiom,
! [B: $i,A: $i,E: $i] :
( ( member @ B @ ( difference @ E @ A ) )
<=> ( ( member @ B @ E )
& ~ ( member @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference) ).
thf(6,axiom,
! [X: $i] :
~ ( member @ X @ empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set) ).
thf(7,axiom,
! [X: $i,A: $i,B: $i] :
( ( member @ X @ ( union @ A @ B ) )
<=> ( ( member @ X @ A )
| ( member @ X @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union) ).
thf(8,axiom,
! [X: $i,A: $i,B: $i] :
( ( member @ X @ ( intersection @ A @ B ) )
<=> ( ( member @ X @ A )
& ( member @ X @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection) ).
thf(9,axiom,
! [X: $i,A: $i] :
( ( member @ X @ ( power_set @ A ) )
<=> ( subset @ X @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_set) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( equal_set @ A @ B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_set) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [X: $i] :
( ( member @ X @ A )
=> ( member @ X @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).
thf(12,conjecture,
! [A: $i,B: $i,E: $i] :
( ( ( subset @ A @ E )
& ( subset @ B @ E ) )
=> ( ( subset @ A @ B )
<=> ( subset @ ( intersection @ A @ ( difference @ E @ B ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI34) ).
thf(13,negated_conjecture,
( ( ! [A: $i,B: $i,E: $i] :
( ( ( subset @ A @ E )
& ( subset @ B @ E ) )
=> ( ( subset @ A @ B )
<=> ( subset @ ( intersection @ A @ ( difference @ E @ B ) ) @ B ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[12]) ).
thf(14,plain,
( ( ! [A: $i,B: $i,E: $i] :
( ( ( subset @ A @ E )
& ( subset @ B @ E ) )
=> ( ( subset @ A @ B )
<=> ( subset @ ( intersection @ A @ ( difference @ E @ B ) ) @ B ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[13]) ).
thf(15,plain,
( ( ! [X: $i,A: $i] :
( ( member @ X @ ( product @ A ) )
<=> ! [Y: $i] :
( ( member @ Y @ A )
=> ( member @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(16,plain,
( ( ! [X: $i,A: $i] :
( ( member @ X @ ( sum @ A ) )
<=> ? [Y: $i] :
( ( member @ Y @ A )
& ( member @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(17,plain,
( ( ! [X: $i,A: $i,B: $i] :
( ( member @ X @ ( unordered_pair @ A @ B ) )
<=> ( ( X = A )
| ( X = B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(18,plain,
( ( ! [X: $i,A: $i] :
( ( member @ X @ ( singleton @ A ) )
<=> ( X = A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(19,plain,
( ( ! [B: $i,A: $i,E: $i] :
( ( member @ B @ ( difference @ E @ A ) )
<=> ( ( member @ B @ E )
& ~ ( member @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(20,plain,
( ( ! [X: $i] :
~ ( member @ X @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(21,plain,
( ( ! [X: $i,A: $i,B: $i] :
( ( member @ X @ ( union @ A @ B ) )
<=> ( ( member @ X @ A )
| ( member @ X @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(22,plain,
( ( ! [X: $i,A: $i,B: $i] :
( ( member @ X @ ( intersection @ A @ B ) )
<=> ( ( member @ X @ A )
& ( member @ X @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(23,plain,
( ( ! [X: $i,A: $i] :
( ( member @ X @ ( power_set @ A ) )
<=> ( subset @ X @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(24,plain,
( ( ! [A: $i,B: $i] :
( ( equal_set @ A @ B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(25,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [X: $i] :
( ( member @ X @ A )
=> ( member @ X @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(26,plain,
( ( ! [SY31: $i,SY32: $i] :
( ( ( subset @ sK1_A @ SY32 )
& ( subset @ SY31 @ SY32 ) )
=> ( ( subset @ sK1_A @ SY31 )
<=> ( subset @ ( intersection @ sK1_A @ ( difference @ SY32 @ SY31 ) ) @ SY31 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[14]) ).
thf(27,plain,
( ( ! [SY33: $i] :
( ( ( subset @ sK1_A @ SY33 )
& ( subset @ sK2_SY31 @ SY33 ) )
=> ( ( subset @ sK1_A @ sK2_SY31 )
<=> ( subset @ ( intersection @ sK1_A @ ( difference @ SY33 @ sK2_SY31 ) ) @ sK2_SY31 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[26]) ).
thf(28,plain,
( ( ( ( subset @ sK1_A @ sK3_SY33 )
& ( subset @ sK2_SY31 @ sK3_SY33 ) )
=> ( ( subset @ sK1_A @ sK2_SY31 )
<=> ( subset @ ( intersection @ sK1_A @ ( difference @ sK3_SY33 @ sK2_SY31 ) ) @ sK2_SY31 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[27]) ).
thf(29,plain,
( ( subset @ sK1_A @ sK3_SY33 )
= $true ),
inference(standard_cnf,[status(thm)],[28]) ).
thf(30,plain,
( ( subset @ sK2_SY31 @ sK3_SY33 )
= $true ),
inference(standard_cnf,[status(thm)],[28]) ).
thf(31,plain,
( ( ( subset @ sK1_A @ sK2_SY31 )
<=> ( subset @ ( intersection @ sK1_A @ ( difference @ sK3_SY33 @ sK2_SY31 ) ) @ sK2_SY31 ) )
= $false ),
inference(standard_cnf,[status(thm)],[28]) ).
thf(32,plain,
( ( ( subset @ sK1_A @ sK2_SY31 )
=> ( subset @ ( intersection @ sK1_A @ ( difference @ sK3_SY33 @ sK2_SY31 ) ) @ sK2_SY31 ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[31]) ).
thf(33,plain,
( ( ( subset @ ( intersection @ sK1_A @ ( difference @ sK3_SY33 @ sK2_SY31 ) ) @ sK2_SY31 )
=> ( subset @ sK1_A @ sK2_SY31 ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[31]) ).
thf(34,plain,
( ( ~ ( ( subset @ sK1_A @ sK2_SY31 )
=> ( subset @ ( intersection @ sK1_A @ ( difference @ sK3_SY33 @ sK2_SY31 ) ) @ sK2_SY31 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[32]) ).
thf(35,plain,
( ( ~ ( ( subset @ ( intersection @ sK1_A @ ( difference @ sK3_SY33 @ sK2_SY31 ) ) @ sK2_SY31 )
=> ( subset @ sK1_A @ sK2_SY31 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[33]) ).
thf(36,plain,
( ( ( subset @ sK1_A @ sK2_SY31 )
& ~ ( subset @ ( intersection @ sK1_A @ ( difference @ sK3_SY33 @ sK2_SY31 ) ) @ sK2_SY31 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[34]) ).
thf(37,plain,
( ( ( subset @ ( intersection @ sK1_A @ ( difference @ sK3_SY33 @ sK2_SY31 ) ) @ sK2_SY31 )
& ~ ( subset @ sK1_A @ sK2_SY31 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[35]) ).
thf(38,plain,
( ( ! [X: $i,A: $i] :
( ( ( member @ ( sK4_Y @ A @ X ) @ A )
& ~ ( member @ X @ ( sK4_Y @ A @ X ) ) )
| ( member @ X @ ( product @ A ) ) )
& ! [X: $i,A: $i] :
( ~ ( member @ X @ ( product @ A ) )
| ! [Y: $i] :
( ~ ( member @ Y @ A )
| ( member @ X @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[15]) ).
thf(39,plain,
( ( ! [X: $i,A: $i] :
( ! [Y: $i] :
( ~ ( member @ Y @ A )
| ~ ( member @ X @ Y ) )
| ( member @ X @ ( sum @ A ) ) )
& ! [X: $i,A: $i] :
( ~ ( member @ X @ ( sum @ A ) )
| ( ( member @ ( sK5_Y @ A @ X ) @ A )
& ( member @ X @ ( sK5_Y @ A @ X ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[16]) ).
thf(40,plain,
( ( ! [X: $i] :
( ! [A: $i,B: $i] :
( ~ ( member @ X @ ( unordered_pair @ A @ B ) )
| ( X = A )
| ( X = B ) )
& ! [A: $i] :
( ( X != A )
| ! [B: $i] : ( member @ X @ ( unordered_pair @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ( X != B )
| ( member @ X @ ( unordered_pair @ A @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[17]) ).
thf(41,plain,
( ( ! [X: $i,A: $i] :
( ( X != A )
| ( member @ X @ ( singleton @ A ) ) )
& ! [X: $i,A: $i] :
( ~ ( member @ X @ ( singleton @ A ) )
| ( X = A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[18]) ).
thf(42,plain,
( ( ! [B: $i] :
( ! [A: $i,E: $i] :
( ~ ( member @ B @ E )
| ( member @ B @ A )
| ( member @ B @ ( difference @ E @ A ) ) )
& ! [A: $i,E: $i] :
( ~ ( member @ B @ ( difference @ E @ A ) )
| ( member @ B @ E ) )
& ! [A: $i] :
( ! [E: $i] :
~ ( member @ B @ ( difference @ E @ A ) )
| ~ ( member @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[19]) ).
thf(43,plain,
( ( ! [X: $i] :
( ! [A: $i,B: $i] :
( ~ ( member @ X @ ( union @ A @ B ) )
| ( member @ X @ A )
| ( member @ X @ B ) )
& ! [A: $i] :
( ~ ( member @ X @ A )
| ! [B: $i] : ( member @ X @ ( union @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( member @ X @ B )
| ( member @ X @ ( union @ A @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[21]) ).
thf(44,plain,
( ( ! [X: $i] :
( ! [A: $i,B: $i] :
( ~ ( member @ X @ A )
| ~ ( member @ X @ B )
| ( member @ X @ ( intersection @ A @ B ) ) )
& ! [A: $i] :
( ! [B: $i] :
~ ( member @ X @ ( intersection @ A @ B ) )
| ( member @ X @ A ) )
& ! [A: $i,B: $i] :
( ~ ( member @ X @ ( intersection @ A @ B ) )
| ( member @ X @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[22]) ).
thf(45,plain,
( ( ! [X: $i,A: $i] :
( ~ ( member @ X @ ( power_set @ A ) )
| ( subset @ X @ A ) )
& ! [X: $i,A: $i] :
( ~ ( subset @ X @ A )
| ( member @ X @ ( power_set @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[23]) ).
thf(46,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( equal_set @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( equal_set @ A @ B )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( equal_set @ A @ B )
| ( subset @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[24]) ).
thf(47,plain,
( ( ! [A: $i,B: $i] :
( ( ( member @ ( sK6_X @ B @ A ) @ A )
& ~ ( member @ ( sK6_X @ B @ A ) @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [X: $i] :
( ~ ( member @ X @ A )
| ( member @ X @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[25]) ).
thf(48,plain,
( ( ! [A: $i,B: $i] :
( ( ( member @ ( sK6_X @ B @ A ) @ A )
& ~ ( member @ ( sK6_X @ B @ A ) @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [X: $i] :
( ~ ( member @ X @ A )
| ( member @ X @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(49,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( equal_set @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( equal_set @ A @ B )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( equal_set @ A @ B )
| ( subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(50,plain,
( ( ! [X: $i,A: $i] :
( ~ ( member @ X @ ( power_set @ A ) )
| ( subset @ X @ A ) )
& ! [X: $i,A: $i] :
( ~ ( subset @ X @ A )
| ( member @ X @ ( power_set @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(51,plain,
( ( ! [X: $i] :
( ! [A: $i,B: $i] :
( ~ ( member @ X @ A )
| ~ ( member @ X @ B )
| ( member @ X @ ( intersection @ A @ B ) ) )
& ! [A: $i] :
( ! [B: $i] :
~ ( member @ X @ ( intersection @ A @ B ) )
| ( member @ X @ A ) )
& ! [A: $i,B: $i] :
( ~ ( member @ X @ ( intersection @ A @ B ) )
| ( member @ X @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(52,plain,
( ( ! [X: $i] :
( ! [A: $i,B: $i] :
( ~ ( member @ X @ ( union @ A @ B ) )
| ( member @ X @ A )
| ( member @ X @ B ) )
& ! [A: $i] :
( ~ ( member @ X @ A )
| ! [B: $i] : ( member @ X @ ( union @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( member @ X @ B )
| ( member @ X @ ( union @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(53,plain,
( ( ! [X: $i] :
~ ( member @ X @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(54,plain,
( ( ! [B: $i] :
( ! [A: $i,E: $i] :
( ~ ( member @ B @ E )
| ( member @ B @ A )
| ( member @ B @ ( difference @ E @ A ) ) )
& ! [A: $i,E: $i] :
( ~ ( member @ B @ ( difference @ E @ A ) )
| ( member @ B @ E ) )
& ! [A: $i] :
( ! [E: $i] :
~ ( member @ B @ ( difference @ E @ A ) )
| ~ ( member @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(55,plain,
( ( ! [X: $i,A: $i] :
( ( X != A )
| ( member @ X @ ( singleton @ A ) ) )
& ! [X: $i,A: $i] :
( ~ ( member @ X @ ( singleton @ A ) )
| ( X = A ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(56,plain,
( ( ! [X: $i] :
( ! [A: $i,B: $i] :
( ~ ( member @ X @ ( unordered_pair @ A @ B ) )
| ( X = A )
| ( X = B ) )
& ! [A: $i] :
( ( X != A )
| ! [B: $i] : ( member @ X @ ( unordered_pair @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ( X != B )
| ( member @ X @ ( unordered_pair @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(57,plain,
( ( ! [X: $i,A: $i] :
( ! [Y: $i] :
( ~ ( member @ Y @ A )
| ~ ( member @ X @ Y ) )
| ( member @ X @ ( sum @ A ) ) )
& ! [X: $i,A: $i] :
( ~ ( member @ X @ ( sum @ A ) )
| ( ( member @ ( sK5_Y @ A @ X ) @ A )
& ( member @ X @ ( sK5_Y @ A @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(58,plain,
( ( ! [X: $i,A: $i] :
( ( ( member @ ( sK4_Y @ A @ X ) @ A )
& ~ ( member @ X @ ( sK4_Y @ A @ X ) ) )
| ( member @ X @ ( product @ A ) ) )
& ! [X: $i,A: $i] :
( ~ ( member @ X @ ( product @ A ) )
| ! [Y: $i] :
( ~ ( member @ Y @ A )
| ( member @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(59,plain,
( ( subset @ sK2_SY31 @ sK3_SY33 )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(60,plain,
( ( subset @ sK1_A @ sK3_SY33 )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(61,plain,
( ( ( subset @ sK1_A @ sK2_SY31 )
& ~ ( subset @ ( intersection @ sK1_A @ ( difference @ sK3_SY33 @ sK2_SY31 ) ) @ sK2_SY31 ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(62,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX0 @ SX1 )
| ~ ( member @ SX0 @ SX2 )
| ( member @ SX0 @ ( intersection @ SX1 @ SX2 ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( member @ SX0 @ ( intersection @ SX1 @ SX2 ) )
| ( member @ SX0 @ SX1 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX0 @ ( intersection @ SX1 @ SX2 ) )
| ( member @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(63,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ~ ( member @ SX0 @ SX2 ) )
| ( member @ SX0 @ ( sum @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( sum @ SX1 ) )
| ~ ( ~ ( member @ ( sK5_Y @ SX1 @ SX0 ) @ SX1 )
| ~ ( member @ SX0 @ ( sK5_Y @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(64,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX0 @ SX2 )
| ( member @ SX0 @ SX1 )
| ( member @ SX0 @ ( difference @ SX2 @ SX1 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX0 @ ( difference @ SX2 @ SX1 ) )
| ( member @ SX0 @ SX2 ) )
| ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( member @ SX0 @ ( difference @ SX2 @ SX1 ) )
| ~ ( member @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(65,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK6_X @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( member @ ( sK6_X @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(66,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK4_Y @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( member @ SX0 @ ( sK4_Y @ SX1 @ SX0 ) ) )
| ( member @ SX0 @ ( product @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( product @ SX1 ) )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( member @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(67,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX0 @ ( unordered_pair @ SX1 @ SX2 ) )
| ( SX0 = SX1 )
| ( SX0 = SX2 ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ( SX0 != SX1 )
| ! [SX2: $i] : ( member @ SX0 @ ( unordered_pair @ SX1 @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX0 != SX2 )
| ( member @ SX0 @ ( unordered_pair @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(68,plain,
( ( ~ ( ~ ( subset @ sK1_A @ sK2_SY31 )
| ~ ~ ( subset @ ( intersection @ sK1_A @ ( difference @ sK3_SY33 @ sK2_SY31 ) ) @ sK2_SY31 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(69,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( member @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(70,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX0 @ ( union @ SX1 @ SX2 ) )
| ( member @ SX0 @ SX1 )
| ( member @ SX0 @ SX2 ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ~ ( member @ SX0 @ SX1 )
| ! [SX2: $i] : ( member @ SX0 @ ( union @ SX1 @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX0 @ SX2 )
| ( member @ SX0 @ ( union @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(71,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( equal_set @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(72,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( power_set @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( member @ SX0 @ ( power_set @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(73,plain,
! [SV1: $i] :
( ( ~ ( member @ SV1 @ empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(74,plain,
! [SV2: $i] :
( ( ~ ( ~ ! [SY34: $i,SY35: $i] :
( ~ ( member @ SV2 @ SY34 )
| ~ ( member @ SV2 @ SY35 )
| ( member @ SV2 @ ( intersection @ SY34 @ SY35 ) ) )
| ~ ~ ( ~ ! [SY36: $i] :
( ! [SY37: $i] :
~ ( member @ SV2 @ ( intersection @ SY36 @ SY37 ) )
| ( member @ SV2 @ SY36 ) )
| ~ ! [SY38: $i,SY39: $i] :
( ~ ( member @ SV2 @ ( intersection @ SY38 @ SY39 ) )
| ( member @ SV2 @ SY39 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(75,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ~ ( member @ SX0 @ SX2 ) )
| ( member @ SX0 @ ( sum @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( sum @ SX1 ) )
| ~ ( ~ ( member @ ( sK5_Y @ SX1 @ SX0 ) @ SX1 )
| ~ ( member @ SX0 @ ( sK5_Y @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(76,plain,
! [SV3: $i] :
( ( ~ ( ~ ! [SY40: $i,SY41: $i] :
( ~ ( member @ SV3 @ SY41 )
| ( member @ SV3 @ SY40 )
| ( member @ SV3 @ ( difference @ SY41 @ SY40 ) ) )
| ~ ~ ( ~ ! [SY42: $i,SY43: $i] :
( ~ ( member @ SV3 @ ( difference @ SY43 @ SY42 ) )
| ( member @ SV3 @ SY43 ) )
| ~ ! [SY44: $i] :
( ! [SY45: $i] :
~ ( member @ SV3 @ ( difference @ SY45 @ SY44 ) )
| ~ ( member @ SV3 @ SY44 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(77,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK6_X @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( member @ ( sK6_X @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(78,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK4_Y @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( member @ SX0 @ ( sK4_Y @ SX1 @ SX0 ) ) )
| ( member @ SX0 @ ( product @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( product @ SX1 ) )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( member @ SX0 @ SX2 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(79,plain,
! [SV4: $i] :
( ( ~ ( ~ ! [SY46: $i,SY47: $i] :
( ~ ( member @ SV4 @ ( unordered_pair @ SY46 @ SY47 ) )
| ( SV4 = SY46 )
| ( SV4 = SY47 ) )
| ~ ~ ( ~ ! [SY48: $i] :
( ( SV4 != SY48 )
| ! [SY49: $i] : ( member @ SV4 @ ( unordered_pair @ SY48 @ SY49 ) ) )
| ~ ! [SY50: $i,SY51: $i] :
( ( SV4 != SY51 )
| ( member @ SV4 @ ( unordered_pair @ SY50 @ SY51 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(80,plain,
( ( ~ ( subset @ sK1_A @ sK2_SY31 )
| ~ ~ ( subset @ ( intersection @ sK1_A @ ( difference @ sK3_SY33 @ sK2_SY31 ) ) @ sK2_SY31 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(81,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( member @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(82,plain,
! [SV5: $i] :
( ( ~ ( ~ ! [SY52: $i,SY53: $i] :
( ~ ( member @ SV5 @ ( union @ SY52 @ SY53 ) )
| ( member @ SV5 @ SY52 )
| ( member @ SV5 @ SY53 ) )
| ~ ~ ( ~ ! [SY54: $i] :
( ~ ( member @ SV5 @ SY54 )
| ! [SY55: $i] : ( member @ SV5 @ ( union @ SY54 @ SY55 ) ) )
| ~ ! [SY56: $i,SY57: $i] :
( ~ ( member @ SV5 @ SY57 )
| ( member @ SV5 @ ( union @ SY56 @ SY57 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(83,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( equal_set @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(84,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( power_set @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( member @ SX0 @ ( power_set @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(85,plain,
! [SV1: $i] :
( ( member @ SV1 @ empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(86,plain,
! [SV2: $i] :
( ( ~ ! [SY34: $i,SY35: $i] :
( ~ ( member @ SV2 @ SY34 )
| ~ ( member @ SV2 @ SY35 )
| ( member @ SV2 @ ( intersection @ SY34 @ SY35 ) ) )
| ~ ~ ( ~ ! [SY36: $i] :
( ! [SY37: $i] :
~ ( member @ SV2 @ ( intersection @ SY36 @ SY37 ) )
| ( member @ SV2 @ SY36 ) )
| ~ ! [SY38: $i,SY39: $i] :
( ~ ( member @ SV2 @ ( intersection @ SY38 @ SY39 ) )
| ( member @ SV2 @ SY39 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(87,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ~ ( member @ SX0 @ SX2 ) )
| ( member @ SX0 @ ( sum @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(88,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( sum @ SX1 ) )
| ~ ( ~ ( member @ ( sK5_Y @ SX1 @ SX0 ) @ SX1 )
| ~ ( member @ SX0 @ ( sK5_Y @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(89,plain,
! [SV3: $i] :
( ( ~ ! [SY40: $i,SY41: $i] :
( ~ ( member @ SV3 @ SY41 )
| ( member @ SV3 @ SY40 )
| ( member @ SV3 @ ( difference @ SY41 @ SY40 ) ) )
| ~ ~ ( ~ ! [SY42: $i,SY43: $i] :
( ~ ( member @ SV3 @ ( difference @ SY43 @ SY42 ) )
| ( member @ SV3 @ SY43 ) )
| ~ ! [SY44: $i] :
( ! [SY45: $i] :
~ ( member @ SV3 @ ( difference @ SY45 @ SY44 ) )
| ~ ( member @ SV3 @ SY44 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(90,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK6_X @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( member @ ( sK6_X @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[77]) ).
thf(91,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[77]) ).
thf(92,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK4_Y @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( member @ SX0 @ ( sK4_Y @ SX1 @ SX0 ) ) )
| ( member @ SX0 @ ( product @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[78]) ).
thf(93,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( product @ SX1 ) )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( member @ SX0 @ SX2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[78]) ).
thf(94,plain,
! [SV4: $i] :
( ( ~ ! [SY46: $i,SY47: $i] :
( ~ ( member @ SV4 @ ( unordered_pair @ SY46 @ SY47 ) )
| ( SV4 = SY46 )
| ( SV4 = SY47 ) )
| ~ ~ ( ~ ! [SY48: $i] :
( ( SV4 != SY48 )
| ! [SY49: $i] : ( member @ SV4 @ ( unordered_pair @ SY48 @ SY49 ) ) )
| ~ ! [SY50: $i,SY51: $i] :
( ( SV4 != SY51 )
| ( member @ SV4 @ ( unordered_pair @ SY50 @ SY51 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(95,plain,
( ( ~ ( subset @ sK1_A @ sK2_SY31 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[80]) ).
thf(96,plain,
( ( ~ ~ ( subset @ ( intersection @ sK1_A @ ( difference @ sK3_SY33 @ sK2_SY31 ) ) @ sK2_SY31 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[80]) ).
thf(97,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( member @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[81]) ).
thf(98,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[81]) ).
thf(99,plain,
! [SV5: $i] :
( ( ~ ! [SY52: $i,SY53: $i] :
( ~ ( member @ SV5 @ ( union @ SY52 @ SY53 ) )
| ( member @ SV5 @ SY52 )
| ( member @ SV5 @ SY53 ) )
| ~ ~ ( ~ ! [SY54: $i] :
( ~ ( member @ SV5 @ SY54 )
| ! [SY55: $i] : ( member @ SV5 @ ( union @ SY54 @ SY55 ) ) )
| ~ ! [SY56: $i,SY57: $i] :
( ~ ( member @ SV5 @ SY57 )
| ( member @ SV5 @ ( union @ SY56 @ SY57 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(100,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( equal_set @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[83]) ).
thf(101,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[83]) ).
thf(102,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( power_set @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[84]) ).
thf(103,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( member @ SX0 @ ( power_set @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[84]) ).
thf(104,plain,
! [SV2: $i] :
( ( ~ ! [SY34: $i,SY35: $i] :
( ~ ( member @ SV2 @ SY34 )
| ~ ( member @ SV2 @ SY35 )
| ( member @ SV2 @ ( intersection @ SY34 @ SY35 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[86]) ).
thf(105,plain,
! [SV2: $i] :
( ( ~ ~ ( ~ ! [SY36: $i] :
( ! [SY37: $i] :
~ ( member @ SV2 @ ( intersection @ SY36 @ SY37 ) )
| ( member @ SV2 @ SY36 ) )
| ~ ! [SY38: $i,SY39: $i] :
( ~ ( member @ SV2 @ ( intersection @ SY38 @ SY39 ) )
| ( member @ SV2 @ SY39 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[86]) ).
thf(106,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ~ ( member @ SX0 @ SX2 ) )
| ( member @ SX0 @ ( sum @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[87]) ).
thf(107,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( sum @ SX1 ) )
| ~ ( ~ ( member @ ( sK5_Y @ SX1 @ SX0 ) @ SX1 )
| ~ ( member @ SX0 @ ( sK5_Y @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[88]) ).
thf(108,plain,
! [SV3: $i] :
( ( ~ ! [SY40: $i,SY41: $i] :
( ~ ( member @ SV3 @ SY41 )
| ( member @ SV3 @ SY40 )
| ( member @ SV3 @ ( difference @ SY41 @ SY40 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[89]) ).
thf(109,plain,
! [SV3: $i] :
( ( ~ ~ ( ~ ! [SY42: $i,SY43: $i] :
( ~ ( member @ SV3 @ ( difference @ SY43 @ SY42 ) )
| ( member @ SV3 @ SY43 ) )
| ~ ! [SY44: $i] :
( ! [SY45: $i] :
~ ( member @ SV3 @ ( difference @ SY45 @ SY44 ) )
| ~ ( member @ SV3 @ SY44 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[89]) ).
thf(110,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK6_X @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( member @ ( sK6_X @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[90]) ).
thf(111,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[91]) ).
thf(112,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK4_Y @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( member @ SX0 @ ( sK4_Y @ SX1 @ SX0 ) ) )
| ( member @ SX0 @ ( product @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[92]) ).
thf(113,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( product @ SX1 ) )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( member @ SX0 @ SX2 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[93]) ).
thf(114,plain,
! [SV4: $i] :
( ( ~ ! [SY46: $i,SY47: $i] :
( ~ ( member @ SV4 @ ( unordered_pair @ SY46 @ SY47 ) )
| ( SV4 = SY46 )
| ( SV4 = SY47 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[94]) ).
thf(115,plain,
! [SV4: $i] :
( ( ~ ~ ( ~ ! [SY48: $i] :
( ( SV4 != SY48 )
| ! [SY49: $i] : ( member @ SV4 @ ( unordered_pair @ SY48 @ SY49 ) ) )
| ~ ! [SY50: $i,SY51: $i] :
( ( SV4 != SY51 )
| ( member @ SV4 @ ( unordered_pair @ SY50 @ SY51 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[94]) ).
thf(116,plain,
( ( subset @ sK1_A @ sK2_SY31 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[95]) ).
thf(117,plain,
( ( ~ ( subset @ ( intersection @ sK1_A @ ( difference @ sK3_SY33 @ sK2_SY31 ) ) @ sK2_SY31 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[96]) ).
thf(118,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( member @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[97]) ).
thf(119,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[98]) ).
thf(120,plain,
! [SV5: $i] :
( ( ~ ! [SY52: $i,SY53: $i] :
( ~ ( member @ SV5 @ ( union @ SY52 @ SY53 ) )
| ( member @ SV5 @ SY52 )
| ( member @ SV5 @ SY53 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[99]) ).
thf(121,plain,
! [SV5: $i] :
( ( ~ ~ ( ~ ! [SY54: $i] :
( ~ ( member @ SV5 @ SY54 )
| ! [SY55: $i] : ( member @ SV5 @ ( union @ SY54 @ SY55 ) ) )
| ~ ! [SY56: $i,SY57: $i] :
( ~ ( member @ SV5 @ SY57 )
| ( member @ SV5 @ ( union @ SY56 @ SY57 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[99]) ).
thf(122,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( equal_set @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[100]) ).
thf(123,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[101]) ).
thf(124,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( power_set @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[102]) ).
thf(125,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( member @ SX0 @ ( power_set @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[103]) ).
thf(126,plain,
! [SV2: $i] :
( ( ! [SY34: $i,SY35: $i] :
( ~ ( member @ SV2 @ SY34 )
| ~ ( member @ SV2 @ SY35 )
| ( member @ SV2 @ ( intersection @ SY34 @ SY35 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[104]) ).
thf(127,plain,
! [SV2: $i] :
( ( ~ ( ~ ! [SY36: $i] :
( ! [SY37: $i] :
~ ( member @ SV2 @ ( intersection @ SY36 @ SY37 ) )
| ( member @ SV2 @ SY36 ) )
| ~ ! [SY38: $i,SY39: $i] :
( ~ ( member @ SV2 @ ( intersection @ SY38 @ SY39 ) )
| ( member @ SV2 @ SY39 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[105]) ).
thf(128,plain,
! [SV6: $i] :
( ( ! [SY58: $i] :
( ! [SY59: $i] :
( ~ ( member @ SY59 @ SY58 )
| ~ ( member @ SV6 @ SY59 ) )
| ( member @ SV6 @ ( sum @ SY58 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(129,plain,
! [SV7: $i] :
( ( ! [SY60: $i] :
( ~ ( member @ SV7 @ ( sum @ SY60 ) )
| ~ ( ~ ( member @ ( sK5_Y @ SY60 @ SV7 ) @ SY60 )
| ~ ( member @ SV7 @ ( sK5_Y @ SY60 @ SV7 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(130,plain,
! [SV3: $i] :
( ( ! [SY40: $i,SY41: $i] :
( ~ ( member @ SV3 @ SY41 )
| ( member @ SV3 @ SY40 )
| ( member @ SV3 @ ( difference @ SY41 @ SY40 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[108]) ).
thf(131,plain,
! [SV3: $i] :
( ( ~ ( ~ ! [SY42: $i,SY43: $i] :
( ~ ( member @ SV3 @ ( difference @ SY43 @ SY42 ) )
| ( member @ SV3 @ SY43 ) )
| ~ ! [SY44: $i] :
( ! [SY45: $i] :
~ ( member @ SV3 @ ( difference @ SY45 @ SY44 ) )
| ~ ( member @ SV3 @ SY44 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[109]) ).
thf(132,plain,
! [SV8: $i] :
( ( ! [SY61: $i] :
( ~ ( ~ ( member @ ( sK6_X @ SY61 @ SV8 ) @ SV8 )
| ~ ~ ( member @ ( sK6_X @ SY61 @ SV8 ) @ SY61 ) )
| ( subset @ SV8 @ SY61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(133,plain,
! [SV9: $i] :
( ( ! [SY62: $i] :
( ~ ( subset @ SV9 @ SY62 )
| ! [SY63: $i] :
( ~ ( member @ SY63 @ SV9 )
| ( member @ SY63 @ SY62 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(134,plain,
! [SV10: $i] :
( ( ! [SY64: $i] :
( ~ ( ~ ( member @ ( sK4_Y @ SY64 @ SV10 ) @ SY64 )
| ~ ~ ( member @ SV10 @ ( sK4_Y @ SY64 @ SV10 ) ) )
| ( member @ SV10 @ ( product @ SY64 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(135,plain,
! [SV11: $i] :
( ( ! [SY65: $i] :
( ~ ( member @ SV11 @ ( product @ SY65 ) )
| ! [SY66: $i] :
( ~ ( member @ SY66 @ SY65 )
| ( member @ SV11 @ SY66 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(136,plain,
! [SV4: $i] :
( ( ! [SY46: $i,SY47: $i] :
( ~ ( member @ SV4 @ ( unordered_pair @ SY46 @ SY47 ) )
| ( SV4 = SY46 )
| ( SV4 = SY47 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[114]) ).
thf(137,plain,
! [SV4: $i] :
( ( ~ ( ~ ! [SY48: $i] :
( ( SV4 != SY48 )
| ! [SY49: $i] : ( member @ SV4 @ ( unordered_pair @ SY48 @ SY49 ) ) )
| ~ ! [SY50: $i,SY51: $i] :
( ( SV4 != SY51 )
| ( member @ SV4 @ ( unordered_pair @ SY50 @ SY51 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[115]) ).
thf(138,plain,
( ( subset @ ( intersection @ sK1_A @ ( difference @ sK3_SY33 @ sK2_SY31 ) ) @ sK2_SY31 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(139,plain,
! [SV12: $i] :
( ( ! [SY67: $i] :
( ( SV12 != SY67 )
| ( member @ SV12 @ ( singleton @ SY67 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(140,plain,
! [SV13: $i] :
( ( ! [SY68: $i] :
( ~ ( member @ SV13 @ ( singleton @ SY68 ) )
| ( SV13 = SY68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(141,plain,
! [SV5: $i] :
( ( ! [SY52: $i,SY53: $i] :
( ~ ( member @ SV5 @ ( union @ SY52 @ SY53 ) )
| ( member @ SV5 @ SY52 )
| ( member @ SV5 @ SY53 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[120]) ).
thf(142,plain,
! [SV5: $i] :
( ( ~ ( ~ ! [SY54: $i] :
( ~ ( member @ SV5 @ SY54 )
| ! [SY55: $i] : ( member @ SV5 @ ( union @ SY54 @ SY55 ) ) )
| ~ ! [SY56: $i,SY57: $i] :
( ~ ( member @ SV5 @ SY57 )
| ( member @ SV5 @ ( union @ SY56 @ SY57 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[121]) ).
thf(143,plain,
! [SV14: $i] :
( ( ! [SY69: $i] :
( ~ ( subset @ SV14 @ SY69 )
| ~ ( subset @ SY69 @ SV14 )
| ( equal_set @ SV14 @ SY69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(144,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(145,plain,
! [SV15: $i] :
( ( ! [SY70: $i] :
( ~ ( member @ SV15 @ ( power_set @ SY70 ) )
| ( subset @ SV15 @ SY70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(146,plain,
! [SV16: $i] :
( ( ! [SY71: $i] :
( ~ ( subset @ SV16 @ SY71 )
| ( member @ SV16 @ ( power_set @ SY71 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(147,plain,
! [SV17: $i,SV2: $i] :
( ( ! [SY72: $i] :
( ~ ( member @ SV2 @ SV17 )
| ~ ( member @ SV2 @ SY72 )
| ( member @ SV2 @ ( intersection @ SV17 @ SY72 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(148,plain,
! [SV2: $i] :
( ( ~ ! [SY36: $i] :
( ! [SY37: $i] :
~ ( member @ SV2 @ ( intersection @ SY36 @ SY37 ) )
| ( member @ SV2 @ SY36 ) )
| ~ ! [SY38: $i,SY39: $i] :
( ~ ( member @ SV2 @ ( intersection @ SY38 @ SY39 ) )
| ( member @ SV2 @ SY39 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(149,plain,
! [SV6: $i,SV18: $i] :
( ( ! [SY73: $i] :
( ~ ( member @ SY73 @ SV18 )
| ~ ( member @ SV6 @ SY73 ) )
| ( member @ SV6 @ ( sum @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(150,plain,
! [SV19: $i,SV7: $i] :
( ( ~ ( member @ SV7 @ ( sum @ SV19 ) )
| ~ ( ~ ( member @ ( sK5_Y @ SV19 @ SV7 ) @ SV19 )
| ~ ( member @ SV7 @ ( sK5_Y @ SV19 @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(151,plain,
! [SV20: $i,SV3: $i] :
( ( ! [SY74: $i] :
( ~ ( member @ SV3 @ SY74 )
| ( member @ SV3 @ SV20 )
| ( member @ SV3 @ ( difference @ SY74 @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(152,plain,
! [SV3: $i] :
( ( ~ ! [SY42: $i,SY43: $i] :
( ~ ( member @ SV3 @ ( difference @ SY43 @ SY42 ) )
| ( member @ SV3 @ SY43 ) )
| ~ ! [SY44: $i] :
( ! [SY45: $i] :
~ ( member @ SV3 @ ( difference @ SY45 @ SY44 ) )
| ~ ( member @ SV3 @ SY44 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(153,plain,
! [SV8: $i,SV21: $i] :
( ( ~ ( ~ ( member @ ( sK6_X @ SV21 @ SV8 ) @ SV8 )
| ~ ~ ( member @ ( sK6_X @ SV21 @ SV8 ) @ SV21 ) )
| ( subset @ SV8 @ SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(154,plain,
! [SV22: $i,SV9: $i] :
( ( ~ ( subset @ SV9 @ SV22 )
| ! [SY75: $i] :
( ~ ( member @ SY75 @ SV9 )
| ( member @ SY75 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(155,plain,
! [SV10: $i,SV23: $i] :
( ( ~ ( ~ ( member @ ( sK4_Y @ SV23 @ SV10 ) @ SV23 )
| ~ ~ ( member @ SV10 @ ( sK4_Y @ SV23 @ SV10 ) ) )
| ( member @ SV10 @ ( product @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(156,plain,
! [SV24: $i,SV11: $i] :
( ( ~ ( member @ SV11 @ ( product @ SV24 ) )
| ! [SY76: $i] :
( ~ ( member @ SY76 @ SV24 )
| ( member @ SV11 @ SY76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(157,plain,
! [SV25: $i,SV4: $i] :
( ( ! [SY77: $i] :
( ~ ( member @ SV4 @ ( unordered_pair @ SV25 @ SY77 ) )
| ( SV4 = SV25 )
| ( SV4 = SY77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(158,plain,
! [SV4: $i] :
( ( ~ ! [SY48: $i] :
( ( SV4 != SY48 )
| ! [SY49: $i] : ( member @ SV4 @ ( unordered_pair @ SY48 @ SY49 ) ) )
| ~ ! [SY50: $i,SY51: $i] :
( ( SV4 != SY51 )
| ( member @ SV4 @ ( unordered_pair @ SY50 @ SY51 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(159,plain,
! [SV26: $i,SV12: $i] :
( ( ( SV12 != SV26 )
| ( member @ SV12 @ ( singleton @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(160,plain,
! [SV27: $i,SV13: $i] :
( ( ~ ( member @ SV13 @ ( singleton @ SV27 ) )
| ( SV13 = SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(161,plain,
! [SV28: $i,SV5: $i] :
( ( ! [SY78: $i] :
( ~ ( member @ SV5 @ ( union @ SV28 @ SY78 ) )
| ( member @ SV5 @ SV28 )
| ( member @ SV5 @ SY78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(162,plain,
! [SV5: $i] :
( ( ~ ! [SY54: $i] :
( ~ ( member @ SV5 @ SY54 )
| ! [SY55: $i] : ( member @ SV5 @ ( union @ SY54 @ SY55 ) ) )
| ~ ! [SY56: $i,SY57: $i] :
( ~ ( member @ SV5 @ SY57 )
| ( member @ SV5 @ ( union @ SY56 @ SY57 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(163,plain,
! [SV29: $i,SV14: $i] :
( ( ~ ( subset @ SV14 @ SV29 )
| ~ ( subset @ SV29 @ SV14 )
| ( equal_set @ SV14 @ SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(164,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[144]) ).
thf(165,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[144]) ).
thf(166,plain,
! [SV30: $i,SV15: $i] :
( ( ~ ( member @ SV15 @ ( power_set @ SV30 ) )
| ( subset @ SV15 @ SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(167,plain,
! [SV31: $i,SV16: $i] :
( ( ~ ( subset @ SV16 @ SV31 )
| ( member @ SV16 @ ( power_set @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(168,plain,
! [SV32: $i,SV17: $i,SV2: $i] :
( ( ~ ( member @ SV2 @ SV17 )
| ~ ( member @ SV2 @ SV32 )
| ( member @ SV2 @ ( intersection @ SV17 @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(169,plain,
! [SV2: $i] :
( ( ~ ! [SY36: $i] :
( ! [SY37: $i] :
~ ( member @ SV2 @ ( intersection @ SY36 @ SY37 ) )
| ( member @ SV2 @ SY36 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[148]) ).
thf(170,plain,
! [SV2: $i] :
( ( ~ ! [SY38: $i,SY39: $i] :
( ~ ( member @ SV2 @ ( intersection @ SY38 @ SY39 ) )
| ( member @ SV2 @ SY39 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[148]) ).
thf(171,plain,
! [SV6: $i,SV18: $i] :
( ( ( ! [SY73: $i] :
( ~ ( member @ SY73 @ SV18 )
| ~ ( member @ SV6 @ SY73 ) ) )
= $true )
| ( ( member @ SV6 @ ( sum @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[149]) ).
thf(172,plain,
! [SV19: $i,SV7: $i] :
( ( ( ~ ( member @ SV7 @ ( sum @ SV19 ) ) )
= $true )
| ( ( ~ ( ~ ( member @ ( sK5_Y @ SV19 @ SV7 ) @ SV19 )
| ~ ( member @ SV7 @ ( sK5_Y @ SV19 @ SV7 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[150]) ).
thf(173,plain,
! [SV20: $i,SV33: $i,SV3: $i] :
( ( ~ ( member @ SV3 @ SV33 )
| ( member @ SV3 @ SV20 )
| ( member @ SV3 @ ( difference @ SV33 @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(174,plain,
! [SV3: $i] :
( ( ~ ! [SY42: $i,SY43: $i] :
( ~ ( member @ SV3 @ ( difference @ SY43 @ SY42 ) )
| ( member @ SV3 @ SY43 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[152]) ).
thf(175,plain,
! [SV3: $i] :
( ( ~ ! [SY44: $i] :
( ! [SY45: $i] :
~ ( member @ SV3 @ ( difference @ SY45 @ SY44 ) )
| ~ ( member @ SV3 @ SY44 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[152]) ).
thf(176,plain,
! [SV8: $i,SV21: $i] :
( ( ( ~ ( ~ ( member @ ( sK6_X @ SV21 @ SV8 ) @ SV8 )
| ~ ~ ( member @ ( sK6_X @ SV21 @ SV8 ) @ SV21 ) ) )
= $true )
| ( ( subset @ SV8 @ SV21 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[153]) ).
thf(177,plain,
! [SV22: $i,SV9: $i] :
( ( ( ~ ( subset @ SV9 @ SV22 ) )
= $true )
| ( ( ! [SY75: $i] :
( ~ ( member @ SY75 @ SV9 )
| ( member @ SY75 @ SV22 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[154]) ).
thf(178,plain,
! [SV10: $i,SV23: $i] :
( ( ( ~ ( ~ ( member @ ( sK4_Y @ SV23 @ SV10 ) @ SV23 )
| ~ ~ ( member @ SV10 @ ( sK4_Y @ SV23 @ SV10 ) ) ) )
= $true )
| ( ( member @ SV10 @ ( product @ SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(179,plain,
! [SV24: $i,SV11: $i] :
( ( ( ~ ( member @ SV11 @ ( product @ SV24 ) ) )
= $true )
| ( ( ! [SY76: $i] :
( ~ ( member @ SY76 @ SV24 )
| ( member @ SV11 @ SY76 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[156]) ).
thf(180,plain,
! [SV34: $i,SV25: $i,SV4: $i] :
( ( ~ ( member @ SV4 @ ( unordered_pair @ SV25 @ SV34 ) )
| ( SV4 = SV25 )
| ( SV4 = SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(181,plain,
! [SV4: $i] :
( ( ~ ! [SY48: $i] :
( ( SV4 != SY48 )
| ! [SY49: $i] : ( member @ SV4 @ ( unordered_pair @ SY48 @ SY49 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[158]) ).
thf(182,plain,
! [SV4: $i] :
( ( ~ ! [SY50: $i,SY51: $i] :
( ( SV4 != SY51 )
| ( member @ SV4 @ ( unordered_pair @ SY50 @ SY51 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[158]) ).
thf(183,plain,
! [SV26: $i,SV12: $i] :
( ( ( ( SV12 != SV26 ) )
= $true )
| ( ( member @ SV12 @ ( singleton @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[159]) ).
thf(184,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ( member @ SV13 @ ( singleton @ SV27 ) ) )
= $true )
| ( ( SV13 = SV27 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[160]) ).
thf(185,plain,
! [SV35: $i,SV28: $i,SV5: $i] :
( ( ~ ( member @ SV5 @ ( union @ SV28 @ SV35 ) )
| ( member @ SV5 @ SV28 )
| ( member @ SV5 @ SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(186,plain,
! [SV5: $i] :
( ( ~ ! [SY54: $i] :
( ~ ( member @ SV5 @ SY54 )
| ! [SY55: $i] : ( member @ SV5 @ ( union @ SY54 @ SY55 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[162]) ).
thf(187,plain,
! [SV5: $i] :
( ( ~ ! [SY56: $i,SY57: $i] :
( ~ ( member @ SV5 @ SY57 )
| ( member @ SV5 @ ( union @ SY56 @ SY57 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[162]) ).
thf(188,plain,
! [SV29: $i,SV14: $i] :
( ( ( ~ ( subset @ SV14 @ SV29 )
| ~ ( subset @ SV29 @ SV14 ) )
= $true )
| ( ( equal_set @ SV14 @ SV29 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[163]) ).
thf(189,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[164]) ).
thf(190,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[165]) ).
thf(191,plain,
! [SV30: $i,SV15: $i] :
( ( ( ~ ( member @ SV15 @ ( power_set @ SV30 ) ) )
= $true )
| ( ( subset @ SV15 @ SV30 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(192,plain,
! [SV31: $i,SV16: $i] :
( ( ( ~ ( subset @ SV16 @ SV31 ) )
= $true )
| ( ( member @ SV16 @ ( power_set @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[167]) ).
thf(193,plain,
! [SV32: $i,SV17: $i,SV2: $i] :
( ( ( ~ ( member @ SV2 @ SV17 )
| ~ ( member @ SV2 @ SV32 ) )
= $true )
| ( ( member @ SV2 @ ( intersection @ SV17 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[168]) ).
thf(194,plain,
! [SV2: $i] :
( ( ! [SY36: $i] :
( ! [SY37: $i] :
~ ( member @ SV2 @ ( intersection @ SY36 @ SY37 ) )
| ( member @ SV2 @ SY36 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[169]) ).
thf(195,plain,
! [SV2: $i] :
( ( ! [SY38: $i,SY39: $i] :
( ~ ( member @ SV2 @ ( intersection @ SY38 @ SY39 ) )
| ( member @ SV2 @ SY39 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[170]) ).
thf(196,plain,
! [SV6: $i,SV18: $i,SV36: $i] :
( ( ( ~ ( member @ SV36 @ SV18 )
| ~ ( member @ SV6 @ SV36 ) )
= $true )
| ( ( member @ SV6 @ ( sum @ SV18 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(197,plain,
! [SV19: $i,SV7: $i] :
( ( ( member @ SV7 @ ( sum @ SV19 ) )
= $false )
| ( ( ~ ( ~ ( member @ ( sK5_Y @ SV19 @ SV7 ) @ SV19 )
| ~ ( member @ SV7 @ ( sK5_Y @ SV19 @ SV7 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(198,plain,
! [SV20: $i,SV33: $i,SV3: $i] :
( ( ( ~ ( member @ SV3 @ SV33 )
| ( member @ SV3 @ SV20 ) )
= $true )
| ( ( member @ SV3 @ ( difference @ SV33 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[173]) ).
thf(199,plain,
! [SV3: $i] :
( ( ! [SY42: $i,SY43: $i] :
( ~ ( member @ SV3 @ ( difference @ SY43 @ SY42 ) )
| ( member @ SV3 @ SY43 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[174]) ).
thf(200,plain,
! [SV3: $i] :
( ( ! [SY44: $i] :
( ! [SY45: $i] :
~ ( member @ SV3 @ ( difference @ SY45 @ SY44 ) )
| ~ ( member @ SV3 @ SY44 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[175]) ).
thf(201,plain,
! [SV8: $i,SV21: $i] :
( ( ( ~ ( member @ ( sK6_X @ SV21 @ SV8 ) @ SV8 )
| ~ ~ ( member @ ( sK6_X @ SV21 @ SV8 ) @ SV21 ) )
= $false )
| ( ( subset @ SV8 @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(202,plain,
! [SV22: $i,SV9: $i] :
( ( ( subset @ SV9 @ SV22 )
= $false )
| ( ( ! [SY75: $i] :
( ~ ( member @ SY75 @ SV9 )
| ( member @ SY75 @ SV22 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(203,plain,
! [SV10: $i,SV23: $i] :
( ( ( ~ ( member @ ( sK4_Y @ SV23 @ SV10 ) @ SV23 )
| ~ ~ ( member @ SV10 @ ( sK4_Y @ SV23 @ SV10 ) ) )
= $false )
| ( ( member @ SV10 @ ( product @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(204,plain,
! [SV24: $i,SV11: $i] :
( ( ( member @ SV11 @ ( product @ SV24 ) )
= $false )
| ( ( ! [SY76: $i] :
( ~ ( member @ SY76 @ SV24 )
| ( member @ SV11 @ SY76 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(205,plain,
! [SV34: $i,SV25: $i,SV4: $i] :
( ( ( ~ ( member @ SV4 @ ( unordered_pair @ SV25 @ SV34 ) ) )
= $true )
| ( ( ( SV4 = SV25 )
| ( SV4 = SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[180]) ).
thf(206,plain,
! [SV4: $i] :
( ( ! [SY48: $i] :
( ( SV4 != SY48 )
| ! [SY49: $i] : ( member @ SV4 @ ( unordered_pair @ SY48 @ SY49 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[181]) ).
thf(207,plain,
! [SV4: $i] :
( ( ! [SY50: $i,SY51: $i] :
( ( SV4 != SY51 )
| ( member @ SV4 @ ( unordered_pair @ SY50 @ SY51 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[182]) ).
thf(208,plain,
! [SV26: $i,SV12: $i] :
( ( ( SV12 = SV26 )
= $false )
| ( ( member @ SV12 @ ( singleton @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[183]) ).
thf(209,plain,
! [SV27: $i,SV13: $i] :
( ( ( member @ SV13 @ ( singleton @ SV27 ) )
= $false )
| ( ( SV13 = SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(210,plain,
! [SV35: $i,SV28: $i,SV5: $i] :
( ( ( ~ ( member @ SV5 @ ( union @ SV28 @ SV35 ) ) )
= $true )
| ( ( ( member @ SV5 @ SV28 )
| ( member @ SV5 @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[185]) ).
thf(211,plain,
! [SV5: $i] :
( ( ! [SY54: $i] :
( ~ ( member @ SV5 @ SY54 )
| ! [SY55: $i] : ( member @ SV5 @ ( union @ SY54 @ SY55 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[186]) ).
thf(212,plain,
! [SV5: $i] :
( ( ! [SY56: $i,SY57: $i] :
( ~ ( member @ SV5 @ SY57 )
| ( member @ SV5 @ ( union @ SY56 @ SY57 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[187]) ).
thf(213,plain,
! [SV29: $i,SV14: $i] :
( ( ( ~ ( subset @ SV14 @ SV29 ) )
= $true )
| ( ( ~ ( subset @ SV29 @ SV14 ) )
= $true )
| ( ( equal_set @ SV14 @ SV29 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[188]) ).
thf(214,plain,
! [SV37: $i] :
( ( ! [SY79: $i] :
( ~ ( equal_set @ SV37 @ SY79 )
| ( subset @ SV37 @ SY79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(215,plain,
! [SV38: $i] :
( ( ! [SY80: $i] :
( ~ ( equal_set @ SV38 @ SY80 )
| ( subset @ SY80 @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(216,plain,
! [SV30: $i,SV15: $i] :
( ( ( member @ SV15 @ ( power_set @ SV30 ) )
= $false )
| ( ( subset @ SV15 @ SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(217,plain,
! [SV31: $i,SV16: $i] :
( ( ( subset @ SV16 @ SV31 )
= $false )
| ( ( member @ SV16 @ ( power_set @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(218,plain,
! [SV32: $i,SV17: $i,SV2: $i] :
( ( ( ~ ( member @ SV2 @ SV17 ) )
= $true )
| ( ( ~ ( member @ SV2 @ SV32 ) )
= $true )
| ( ( member @ SV2 @ ( intersection @ SV17 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[193]) ).
thf(219,plain,
! [SV39: $i,SV2: $i] :
( ( ! [SY81: $i] :
~ ( member @ SV2 @ ( intersection @ SV39 @ SY81 ) )
| ( member @ SV2 @ SV39 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(220,plain,
! [SV40: $i,SV2: $i] :
( ( ! [SY82: $i] :
( ~ ( member @ SV2 @ ( intersection @ SV40 @ SY82 ) )
| ( member @ SV2 @ SY82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(221,plain,
! [SV6: $i,SV18: $i,SV36: $i] :
( ( ( ~ ( member @ SV36 @ SV18 ) )
= $true )
| ( ( ~ ( member @ SV6 @ SV36 ) )
= $true )
| ( ( member @ SV6 @ ( sum @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[196]) ).
thf(222,plain,
! [SV7: $i,SV19: $i] :
( ( ( ~ ( member @ ( sK5_Y @ SV19 @ SV7 ) @ SV19 )
| ~ ( member @ SV7 @ ( sK5_Y @ SV19 @ SV7 ) ) )
= $false )
| ( ( member @ SV7 @ ( sum @ SV19 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(223,plain,
! [SV20: $i,SV33: $i,SV3: $i] :
( ( ( ~ ( member @ SV3 @ SV33 ) )
= $true )
| ( ( member @ SV3 @ SV20 )
= $true )
| ( ( member @ SV3 @ ( difference @ SV33 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[198]) ).
thf(224,plain,
! [SV41: $i,SV3: $i] :
( ( ! [SY83: $i] :
( ~ ( member @ SV3 @ ( difference @ SY83 @ SV41 ) )
| ( member @ SV3 @ SY83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(225,plain,
! [SV42: $i,SV3: $i] :
( ( ! [SY84: $i] :
~ ( member @ SV3 @ ( difference @ SY84 @ SV42 ) )
| ~ ( member @ SV3 @ SV42 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(226,plain,
! [SV8: $i,SV21: $i] :
( ( ( ~ ( member @ ( sK6_X @ SV21 @ SV8 ) @ SV8 ) )
= $false )
| ( ( subset @ SV8 @ SV21 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[201]) ).
thf(227,plain,
! [SV8: $i,SV21: $i] :
( ( ( ~ ~ ( member @ ( sK6_X @ SV21 @ SV8 ) @ SV21 ) )
= $false )
| ( ( subset @ SV8 @ SV21 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[201]) ).
thf(228,plain,
! [SV22: $i,SV9: $i,SV43: $i] :
( ( ( ~ ( member @ SV43 @ SV9 )
| ( member @ SV43 @ SV22 ) )
= $true )
| ( ( subset @ SV9 @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(229,plain,
! [SV10: $i,SV23: $i] :
( ( ( ~ ( member @ ( sK4_Y @ SV23 @ SV10 ) @ SV23 ) )
= $false )
| ( ( member @ SV10 @ ( product @ SV23 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[203]) ).
thf(230,plain,
! [SV23: $i,SV10: $i] :
( ( ( ~ ~ ( member @ SV10 @ ( sK4_Y @ SV23 @ SV10 ) ) )
= $false )
| ( ( member @ SV10 @ ( product @ SV23 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[203]) ).
thf(231,plain,
! [SV11: $i,SV24: $i,SV44: $i] :
( ( ( ~ ( member @ SV44 @ SV24 )
| ( member @ SV11 @ SV44 ) )
= $true )
| ( ( member @ SV11 @ ( product @ SV24 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(232,plain,
! [SV34: $i,SV25: $i,SV4: $i] :
( ( ( member @ SV4 @ ( unordered_pair @ SV25 @ SV34 ) )
= $false )
| ( ( ( SV4 = SV25 )
| ( SV4 = SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(233,plain,
! [SV45: $i,SV4: $i] :
( ( ( SV4 != SV45 )
| ! [SY85: $i] : ( member @ SV4 @ ( unordered_pair @ SV45 @ SY85 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(234,plain,
! [SV46: $i,SV4: $i] :
( ( ! [SY86: $i] :
( ( SV4 != SY86 )
| ( member @ SV4 @ ( unordered_pair @ SV46 @ SY86 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(235,plain,
! [SV35: $i,SV28: $i,SV5: $i] :
( ( ( member @ SV5 @ ( union @ SV28 @ SV35 ) )
= $false )
| ( ( ( member @ SV5 @ SV28 )
| ( member @ SV5 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(236,plain,
! [SV47: $i,SV5: $i] :
( ( ~ ( member @ SV5 @ SV47 )
| ! [SY87: $i] : ( member @ SV5 @ ( union @ SV47 @ SY87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[211]) ).
thf(237,plain,
! [SV48: $i,SV5: $i] :
( ( ! [SY88: $i] :
( ~ ( member @ SV5 @ SY88 )
| ( member @ SV5 @ ( union @ SV48 @ SY88 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(238,plain,
! [SV29: $i,SV14: $i] :
( ( ( subset @ SV14 @ SV29 )
= $false )
| ( ( ~ ( subset @ SV29 @ SV14 ) )
= $true )
| ( ( equal_set @ SV14 @ SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(239,plain,
! [SV49: $i,SV37: $i] :
( ( ~ ( equal_set @ SV37 @ SV49 )
| ( subset @ SV37 @ SV49 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[214]) ).
thf(240,plain,
! [SV50: $i,SV38: $i] :
( ( ~ ( equal_set @ SV38 @ SV50 )
| ( subset @ SV50 @ SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(241,plain,
! [SV32: $i,SV17: $i,SV2: $i] :
( ( ( member @ SV2 @ SV17 )
= $false )
| ( ( ~ ( member @ SV2 @ SV32 ) )
= $true )
| ( ( member @ SV2 @ ( intersection @ SV17 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(242,plain,
! [SV39: $i,SV2: $i] :
( ( ( ! [SY81: $i] :
~ ( member @ SV2 @ ( intersection @ SV39 @ SY81 ) ) )
= $true )
| ( ( member @ SV2 @ SV39 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[219]) ).
thf(243,plain,
! [SV51: $i,SV40: $i,SV2: $i] :
( ( ~ ( member @ SV2 @ ( intersection @ SV40 @ SV51 ) )
| ( member @ SV2 @ SV51 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(244,plain,
! [SV6: $i,SV18: $i,SV36: $i] :
( ( ( member @ SV36 @ SV18 )
= $false )
| ( ( ~ ( member @ SV6 @ SV36 ) )
= $true )
| ( ( member @ SV6 @ ( sum @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(245,plain,
! [SV7: $i,SV19: $i] :
( ( ( ~ ( member @ ( sK5_Y @ SV19 @ SV7 ) @ SV19 ) )
= $false )
| ( ( member @ SV7 @ ( sum @ SV19 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[222]) ).
thf(246,plain,
! [SV19: $i,SV7: $i] :
( ( ( ~ ( member @ SV7 @ ( sK5_Y @ SV19 @ SV7 ) ) )
= $false )
| ( ( member @ SV7 @ ( sum @ SV19 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[222]) ).
thf(247,plain,
! [SV20: $i,SV33: $i,SV3: $i] :
( ( ( member @ SV3 @ SV33 )
= $false )
| ( ( member @ SV3 @ SV20 )
= $true )
| ( ( member @ SV3 @ ( difference @ SV33 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(248,plain,
! [SV41: $i,SV52: $i,SV3: $i] :
( ( ~ ( member @ SV3 @ ( difference @ SV52 @ SV41 ) )
| ( member @ SV3 @ SV52 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[224]) ).
thf(249,plain,
! [SV42: $i,SV3: $i] :
( ( ( ! [SY84: $i] :
~ ( member @ SV3 @ ( difference @ SY84 @ SV42 ) ) )
= $true )
| ( ( ~ ( member @ SV3 @ SV42 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[225]) ).
thf(250,plain,
! [SV8: $i,SV21: $i] :
( ( ( member @ ( sK6_X @ SV21 @ SV8 ) @ SV8 )
= $true )
| ( ( subset @ SV8 @ SV21 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[226]) ).
thf(251,plain,
! [SV8: $i,SV21: $i] :
( ( ( ~ ( member @ ( sK6_X @ SV21 @ SV8 ) @ SV21 ) )
= $true )
| ( ( subset @ SV8 @ SV21 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[227]) ).
thf(252,plain,
! [SV22: $i,SV9: $i,SV43: $i] :
( ( ( ~ ( member @ SV43 @ SV9 ) )
= $true )
| ( ( member @ SV43 @ SV22 )
= $true )
| ( ( subset @ SV9 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[228]) ).
thf(253,plain,
! [SV10: $i,SV23: $i] :
( ( ( member @ ( sK4_Y @ SV23 @ SV10 ) @ SV23 )
= $true )
| ( ( member @ SV10 @ ( product @ SV23 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[229]) ).
thf(254,plain,
! [SV23: $i,SV10: $i] :
( ( ( ~ ( member @ SV10 @ ( sK4_Y @ SV23 @ SV10 ) ) )
= $true )
| ( ( member @ SV10 @ ( product @ SV23 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[230]) ).
thf(255,plain,
! [SV11: $i,SV24: $i,SV44: $i] :
( ( ( ~ ( member @ SV44 @ SV24 ) )
= $true )
| ( ( member @ SV11 @ SV44 )
= $true )
| ( ( member @ SV11 @ ( product @ SV24 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[231]) ).
thf(256,plain,
! [SV34: $i,SV25: $i,SV4: $i] :
( ( ( SV4 = SV25 )
= $true )
| ( ( SV4 = SV34 )
= $true )
| ( ( member @ SV4 @ ( unordered_pair @ SV25 @ SV34 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[232]) ).
thf(257,plain,
! [SV45: $i,SV4: $i] :
( ( ( ( SV4 != SV45 ) )
= $true )
| ( ( ! [SY85: $i] : ( member @ SV4 @ ( unordered_pair @ SV45 @ SY85 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[233]) ).
thf(258,plain,
! [SV46: $i,SV53: $i,SV4: $i] :
( ( ( SV4 != SV53 )
| ( member @ SV4 @ ( unordered_pair @ SV46 @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[234]) ).
thf(259,plain,
! [SV35: $i,SV28: $i,SV5: $i] :
( ( ( member @ SV5 @ SV28 )
= $true )
| ( ( member @ SV5 @ SV35 )
= $true )
| ( ( member @ SV5 @ ( union @ SV28 @ SV35 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[235]) ).
thf(260,plain,
! [SV47: $i,SV5: $i] :
( ( ( ~ ( member @ SV5 @ SV47 ) )
= $true )
| ( ( ! [SY87: $i] : ( member @ SV5 @ ( union @ SV47 @ SY87 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[236]) ).
thf(261,plain,
! [SV48: $i,SV54: $i,SV5: $i] :
( ( ~ ( member @ SV5 @ SV54 )
| ( member @ SV5 @ ( union @ SV48 @ SV54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[237]) ).
thf(262,plain,
! [SV14: $i,SV29: $i] :
( ( ( subset @ SV29 @ SV14 )
= $false )
| ( ( subset @ SV14 @ SV29 )
= $false )
| ( ( equal_set @ SV14 @ SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(263,plain,
! [SV49: $i,SV37: $i] :
( ( ( ~ ( equal_set @ SV37 @ SV49 ) )
= $true )
| ( ( subset @ SV37 @ SV49 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[239]) ).
thf(264,plain,
! [SV50: $i,SV38: $i] :
( ( ( ~ ( equal_set @ SV38 @ SV50 ) )
= $true )
| ( ( subset @ SV50 @ SV38 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[240]) ).
thf(265,plain,
! [SV17: $i,SV32: $i,SV2: $i] :
( ( ( member @ SV2 @ SV32 )
= $false )
| ( ( member @ SV2 @ SV17 )
= $false )
| ( ( member @ SV2 @ ( intersection @ SV17 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(266,plain,
! [SV55: $i,SV39: $i,SV2: $i] :
( ( ( ~ ( member @ SV2 @ ( intersection @ SV39 @ SV55 ) ) )
= $true )
| ( ( member @ SV2 @ SV39 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[242]) ).
thf(267,plain,
! [SV51: $i,SV40: $i,SV2: $i] :
( ( ( ~ ( member @ SV2 @ ( intersection @ SV40 @ SV51 ) ) )
= $true )
| ( ( member @ SV2 @ SV51 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[243]) ).
thf(268,plain,
! [SV18: $i,SV36: $i,SV6: $i] :
( ( ( member @ SV6 @ SV36 )
= $false )
| ( ( member @ SV36 @ SV18 )
= $false )
| ( ( member @ SV6 @ ( sum @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(269,plain,
! [SV7: $i,SV19: $i] :
( ( ( member @ ( sK5_Y @ SV19 @ SV7 ) @ SV19 )
= $true )
| ( ( member @ SV7 @ ( sum @ SV19 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[245]) ).
thf(270,plain,
! [SV19: $i,SV7: $i] :
( ( ( member @ SV7 @ ( sK5_Y @ SV19 @ SV7 ) )
= $true )
| ( ( member @ SV7 @ ( sum @ SV19 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[246]) ).
thf(271,plain,
! [SV41: $i,SV52: $i,SV3: $i] :
( ( ( ~ ( member @ SV3 @ ( difference @ SV52 @ SV41 ) ) )
= $true )
| ( ( member @ SV3 @ SV52 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[248]) ).
thf(272,plain,
! [SV42: $i,SV56: $i,SV3: $i] :
( ( ( ~ ( member @ SV3 @ ( difference @ SV56 @ SV42 ) ) )
= $true )
| ( ( ~ ( member @ SV3 @ SV42 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[249]) ).
thf(273,plain,
! [SV8: $i,SV21: $i] :
( ( ( member @ ( sK6_X @ SV21 @ SV8 ) @ SV21 )
= $false )
| ( ( subset @ SV8 @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[251]) ).
thf(274,plain,
! [SV22: $i,SV9: $i,SV43: $i] :
( ( ( member @ SV43 @ SV9 )
= $false )
| ( ( member @ SV43 @ SV22 )
= $true )
| ( ( subset @ SV9 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[252]) ).
thf(275,plain,
! [SV23: $i,SV10: $i] :
( ( ( member @ SV10 @ ( sK4_Y @ SV23 @ SV10 ) )
= $false )
| ( ( member @ SV10 @ ( product @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[254]) ).
thf(276,plain,
! [SV11: $i,SV24: $i,SV44: $i] :
( ( ( member @ SV44 @ SV24 )
= $false )
| ( ( member @ SV11 @ SV44 )
= $true )
| ( ( member @ SV11 @ ( product @ SV24 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[255]) ).
thf(277,plain,
! [SV45: $i,SV4: $i] :
( ( ( SV4 = SV45 )
= $false )
| ( ( ! [SY85: $i] : ( member @ SV4 @ ( unordered_pair @ SV45 @ SY85 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(278,plain,
! [SV46: $i,SV53: $i,SV4: $i] :
( ( ( ( SV4 != SV53 ) )
= $true )
| ( ( member @ SV4 @ ( unordered_pair @ SV46 @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[258]) ).
thf(279,plain,
! [SV47: $i,SV5: $i] :
( ( ( member @ SV5 @ SV47 )
= $false )
| ( ( ! [SY87: $i] : ( member @ SV5 @ ( union @ SV47 @ SY87 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[260]) ).
thf(280,plain,
! [SV48: $i,SV54: $i,SV5: $i] :
( ( ( ~ ( member @ SV5 @ SV54 ) )
= $true )
| ( ( member @ SV5 @ ( union @ SV48 @ SV54 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[261]) ).
thf(281,plain,
! [SV49: $i,SV37: $i] :
( ( ( equal_set @ SV37 @ SV49 )
= $false )
| ( ( subset @ SV37 @ SV49 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(282,plain,
! [SV50: $i,SV38: $i] :
( ( ( equal_set @ SV38 @ SV50 )
= $false )
| ( ( subset @ SV50 @ SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[264]) ).
thf(283,plain,
! [SV55: $i,SV39: $i,SV2: $i] :
( ( ( member @ SV2 @ ( intersection @ SV39 @ SV55 ) )
= $false )
| ( ( member @ SV2 @ SV39 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[266]) ).
thf(284,plain,
! [SV51: $i,SV40: $i,SV2: $i] :
( ( ( member @ SV2 @ ( intersection @ SV40 @ SV51 ) )
= $false )
| ( ( member @ SV2 @ SV51 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[267]) ).
thf(285,plain,
! [SV41: $i,SV52: $i,SV3: $i] :
( ( ( member @ SV3 @ ( difference @ SV52 @ SV41 ) )
= $false )
| ( ( member @ SV3 @ SV52 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[271]) ).
thf(286,plain,
! [SV42: $i,SV56: $i,SV3: $i] :
( ( ( member @ SV3 @ ( difference @ SV56 @ SV42 ) )
= $false )
| ( ( ~ ( member @ SV3 @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[272]) ).
thf(287,plain,
! [SV57: $i,SV45: $i,SV4: $i] :
( ( ( member @ SV4 @ ( unordered_pair @ SV45 @ SV57 ) )
= $true )
| ( ( SV4 = SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[277]) ).
thf(288,plain,
! [SV46: $i,SV53: $i,SV4: $i] :
( ( ( SV4 = SV53 )
= $false )
| ( ( member @ SV4 @ ( unordered_pair @ SV46 @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(289,plain,
! [SV58: $i,SV47: $i,SV5: $i] :
( ( ( member @ SV5 @ ( union @ SV47 @ SV58 ) )
= $true )
| ( ( member @ SV5 @ SV47 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[279]) ).
thf(290,plain,
! [SV48: $i,SV54: $i,SV5: $i] :
( ( ( member @ SV5 @ SV54 )
= $false )
| ( ( member @ SV5 @ ( union @ SV48 @ SV54 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[280]) ).
thf(291,plain,
! [SV56: $i,SV42: $i,SV3: $i] :
( ( ( member @ SV3 @ SV42 )
= $false )
| ( ( member @ SV3 @ ( difference @ SV56 @ SV42 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[286]) ).
thf(292,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[59,291,290,289,288,287,285,284,283,282,281,276,275,274,273,270,269,268,265,262,259,256,253,250,247,217,216,209,208,138,116,85,60]) ).
thf(293,plain,
( ( ! [A: $i,B: $i] :
( ( ( member @ ( sK6_X @ B @ A ) @ A )
& ~ ( member @ ( sK6_X @ B @ A ) @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [X: $i] :
( ~ ( member @ X @ A )
| ( member @ X @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(294,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( equal_set @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( equal_set @ A @ B )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( equal_set @ A @ B )
| ( subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(295,plain,
( ( ! [X: $i,A: $i] :
( ~ ( member @ X @ ( power_set @ A ) )
| ( subset @ X @ A ) )
& ! [X: $i,A: $i] :
( ~ ( subset @ X @ A )
| ( member @ X @ ( power_set @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(296,plain,
( ( ! [X: $i] :
( ! [A: $i,B: $i] :
( ~ ( member @ X @ A )
| ~ ( member @ X @ B )
| ( member @ X @ ( intersection @ A @ B ) ) )
& ! [A: $i] :
( ! [B: $i] :
~ ( member @ X @ ( intersection @ A @ B ) )
| ( member @ X @ A ) )
& ! [A: $i,B: $i] :
( ~ ( member @ X @ ( intersection @ A @ B ) )
| ( member @ X @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(297,plain,
( ( ! [X: $i] :
( ! [A: $i,B: $i] :
( ~ ( member @ X @ ( union @ A @ B ) )
| ( member @ X @ A )
| ( member @ X @ B ) )
& ! [A: $i] :
( ~ ( member @ X @ A )
| ! [B: $i] : ( member @ X @ ( union @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( member @ X @ B )
| ( member @ X @ ( union @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(298,plain,
( ( ! [X: $i] :
~ ( member @ X @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(299,plain,
( ( ! [B: $i] :
( ! [A: $i,E: $i] :
( ~ ( member @ B @ E )
| ( member @ B @ A )
| ( member @ B @ ( difference @ E @ A ) ) )
& ! [A: $i,E: $i] :
( ~ ( member @ B @ ( difference @ E @ A ) )
| ( member @ B @ E ) )
& ! [A: $i] :
( ! [E: $i] :
~ ( member @ B @ ( difference @ E @ A ) )
| ~ ( member @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(300,plain,
( ( ! [X: $i,A: $i] :
( ( X != A )
| ( member @ X @ ( singleton @ A ) ) )
& ! [X: $i,A: $i] :
( ~ ( member @ X @ ( singleton @ A ) )
| ( X = A ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(301,plain,
( ( ! [X: $i] :
( ! [A: $i,B: $i] :
( ~ ( member @ X @ ( unordered_pair @ A @ B ) )
| ( X = A )
| ( X = B ) )
& ! [A: $i] :
( ( X != A )
| ! [B: $i] : ( member @ X @ ( unordered_pair @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ( X != B )
| ( member @ X @ ( unordered_pair @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(302,plain,
( ( ! [X: $i,A: $i] :
( ! [Y: $i] :
( ~ ( member @ Y @ A )
| ~ ( member @ X @ Y ) )
| ( member @ X @ ( sum @ A ) ) )
& ! [X: $i,A: $i] :
( ~ ( member @ X @ ( sum @ A ) )
| ( ( member @ ( sK5_Y @ A @ X ) @ A )
& ( member @ X @ ( sK5_Y @ A @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(303,plain,
( ( ! [X: $i,A: $i] :
( ( ( member @ ( sK4_Y @ A @ X ) @ A )
& ~ ( member @ X @ ( sK4_Y @ A @ X ) ) )
| ( member @ X @ ( product @ A ) ) )
& ! [X: $i,A: $i] :
( ~ ( member @ X @ ( product @ A ) )
| ! [Y: $i] :
( ~ ( member @ Y @ A )
| ( member @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(304,plain,
( ( subset @ sK2_SY31 @ sK3_SY33 )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(305,plain,
( ( subset @ sK1_A @ sK3_SY33 )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(306,plain,
( ( ( subset @ ( intersection @ sK1_A @ ( difference @ sK3_SY33 @ sK2_SY31 ) ) @ sK2_SY31 )
& ~ ( subset @ sK1_A @ sK2_SY31 ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(307,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( member @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[300]) ).
thf(308,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX0 @ SX2 )
| ( member @ SX0 @ SX1 )
| ( member @ SX0 @ ( difference @ SX2 @ SX1 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX0 @ ( difference @ SX2 @ SX1 ) )
| ( member @ SX0 @ SX2 ) )
| ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( member @ SX0 @ ( difference @ SX2 @ SX1 ) )
| ~ ( member @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[299]) ).
thf(309,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX0 @ SX1 )
| ~ ( member @ SX0 @ SX2 )
| ( member @ SX0 @ ( intersection @ SX1 @ SX2 ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( member @ SX0 @ ( intersection @ SX1 @ SX2 ) )
| ( member @ SX0 @ SX1 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX0 @ ( intersection @ SX1 @ SX2 ) )
| ( member @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[296]) ).
thf(310,plain,
( ( ~ ( ~ ( subset @ ( intersection @ sK1_A @ ( difference @ sK3_SY33 @ sK2_SY31 ) ) @ sK2_SY31 )
| ~ ~ ( subset @ sK1_A @ sK2_SY31 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[306]) ).
thf(311,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX0 @ ( unordered_pair @ SX1 @ SX2 ) )
| ( SX0 = SX1 )
| ( SX0 = SX2 ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ( SX0 != SX1 )
| ! [SX2: $i] : ( member @ SX0 @ ( unordered_pair @ SX1 @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX0 != SX2 )
| ( member @ SX0 @ ( unordered_pair @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[301]) ).
thf(312,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK6_X @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( member @ ( sK6_X @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[293]) ).
thf(313,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK4_Y @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( member @ SX0 @ ( sK4_Y @ SX1 @ SX0 ) ) )
| ( member @ SX0 @ ( product @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( product @ SX1 ) )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( member @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[303]) ).
thf(314,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( equal_set @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[294]) ).
thf(315,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( power_set @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( member @ SX0 @ ( power_set @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[295]) ).
thf(316,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX0 @ ( union @ SX1 @ SX2 ) )
| ( member @ SX0 @ SX1 )
| ( member @ SX0 @ SX2 ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ~ ( member @ SX0 @ SX1 )
| ! [SX2: $i] : ( member @ SX0 @ ( union @ SX1 @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX0 @ SX2 )
| ( member @ SX0 @ ( union @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[297]) ).
thf(317,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ~ ( member @ SX0 @ SX2 ) )
| ( member @ SX0 @ ( sum @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( sum @ SX1 ) )
| ~ ( ~ ( member @ ( sK5_Y @ SX1 @ SX0 ) @ SX1 )
| ~ ( member @ SX0 @ ( sK5_Y @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[302]) ).
thf(318,plain,
! [SV59: $i] :
( ( ~ ( member @ SV59 @ empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[298]) ).
thf(319,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( member @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[307]) ).
thf(320,plain,
! [SV60: $i] :
( ( ~ ( ~ ! [SY89: $i,SY90: $i] :
( ~ ( member @ SV60 @ SY90 )
| ( member @ SV60 @ SY89 )
| ( member @ SV60 @ ( difference @ SY90 @ SY89 ) ) )
| ~ ~ ( ~ ! [SY91: $i,SY92: $i] :
( ~ ( member @ SV60 @ ( difference @ SY92 @ SY91 ) )
| ( member @ SV60 @ SY92 ) )
| ~ ! [SY93: $i] :
( ! [SY94: $i] :
~ ( member @ SV60 @ ( difference @ SY94 @ SY93 ) )
| ~ ( member @ SV60 @ SY93 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[308]) ).
thf(321,plain,
! [SV61: $i] :
( ( ~ ( ~ ! [SY95: $i,SY96: $i] :
( ~ ( member @ SV61 @ SY95 )
| ~ ( member @ SV61 @ SY96 )
| ( member @ SV61 @ ( intersection @ SY95 @ SY96 ) ) )
| ~ ~ ( ~ ! [SY97: $i] :
( ! [SY98: $i] :
~ ( member @ SV61 @ ( intersection @ SY97 @ SY98 ) )
| ( member @ SV61 @ SY97 ) )
| ~ ! [SY99: $i,SY100: $i] :
( ~ ( member @ SV61 @ ( intersection @ SY99 @ SY100 ) )
| ( member @ SV61 @ SY100 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[309]) ).
thf(322,plain,
( ( ~ ( subset @ ( intersection @ sK1_A @ ( difference @ sK3_SY33 @ sK2_SY31 ) ) @ sK2_SY31 )
| ~ ~ ( subset @ sK1_A @ sK2_SY31 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[310]) ).
thf(323,plain,
! [SV62: $i] :
( ( ~ ( ~ ! [SY101: $i,SY102: $i] :
( ~ ( member @ SV62 @ ( unordered_pair @ SY101 @ SY102 ) )
| ( SV62 = SY101 )
| ( SV62 = SY102 ) )
| ~ ~ ( ~ ! [SY103: $i] :
( ( SV62 != SY103 )
| ! [SY104: $i] : ( member @ SV62 @ ( unordered_pair @ SY103 @ SY104 ) ) )
| ~ ! [SY105: $i,SY106: $i] :
( ( SV62 != SY106 )
| ( member @ SV62 @ ( unordered_pair @ SY105 @ SY106 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[311]) ).
thf(324,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK6_X @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( member @ ( sK6_X @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[312]) ).
thf(325,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK4_Y @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( member @ SX0 @ ( sK4_Y @ SX1 @ SX0 ) ) )
| ( member @ SX0 @ ( product @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( product @ SX1 ) )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( member @ SX0 @ SX2 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[313]) ).
thf(326,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( equal_set @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[314]) ).
thf(327,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( power_set @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( member @ SX0 @ ( power_set @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[315]) ).
thf(328,plain,
! [SV63: $i] :
( ( ~ ( ~ ! [SY107: $i,SY108: $i] :
( ~ ( member @ SV63 @ ( union @ SY107 @ SY108 ) )
| ( member @ SV63 @ SY107 )
| ( member @ SV63 @ SY108 ) )
| ~ ~ ( ~ ! [SY109: $i] :
( ~ ( member @ SV63 @ SY109 )
| ! [SY110: $i] : ( member @ SV63 @ ( union @ SY109 @ SY110 ) ) )
| ~ ! [SY111: $i,SY112: $i] :
( ~ ( member @ SV63 @ SY112 )
| ( member @ SV63 @ ( union @ SY111 @ SY112 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[316]) ).
thf(329,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ~ ( member @ SX0 @ SX2 ) )
| ( member @ SX0 @ ( sum @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( sum @ SX1 ) )
| ~ ( ~ ( member @ ( sK5_Y @ SX1 @ SX0 ) @ SX1 )
| ~ ( member @ SX0 @ ( sK5_Y @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[317]) ).
thf(330,plain,
! [SV59: $i] :
( ( member @ SV59 @ empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[318]) ).
thf(331,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( member @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[319]) ).
thf(332,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[319]) ).
thf(333,plain,
! [SV60: $i] :
( ( ~ ! [SY89: $i,SY90: $i] :
( ~ ( member @ SV60 @ SY90 )
| ( member @ SV60 @ SY89 )
| ( member @ SV60 @ ( difference @ SY90 @ SY89 ) ) )
| ~ ~ ( ~ ! [SY91: $i,SY92: $i] :
( ~ ( member @ SV60 @ ( difference @ SY92 @ SY91 ) )
| ( member @ SV60 @ SY92 ) )
| ~ ! [SY93: $i] :
( ! [SY94: $i] :
~ ( member @ SV60 @ ( difference @ SY94 @ SY93 ) )
| ~ ( member @ SV60 @ SY93 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[320]) ).
thf(334,plain,
! [SV61: $i] :
( ( ~ ! [SY95: $i,SY96: $i] :
( ~ ( member @ SV61 @ SY95 )
| ~ ( member @ SV61 @ SY96 )
| ( member @ SV61 @ ( intersection @ SY95 @ SY96 ) ) )
| ~ ~ ( ~ ! [SY97: $i] :
( ! [SY98: $i] :
~ ( member @ SV61 @ ( intersection @ SY97 @ SY98 ) )
| ( member @ SV61 @ SY97 ) )
| ~ ! [SY99: $i,SY100: $i] :
( ~ ( member @ SV61 @ ( intersection @ SY99 @ SY100 ) )
| ( member @ SV61 @ SY100 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[321]) ).
thf(335,plain,
( ( ~ ( subset @ ( intersection @ sK1_A @ ( difference @ sK3_SY33 @ sK2_SY31 ) ) @ sK2_SY31 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[322]) ).
thf(336,plain,
( ( ~ ~ ( subset @ sK1_A @ sK2_SY31 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[322]) ).
thf(337,plain,
! [SV62: $i] :
( ( ~ ! [SY101: $i,SY102: $i] :
( ~ ( member @ SV62 @ ( unordered_pair @ SY101 @ SY102 ) )
| ( SV62 = SY101 )
| ( SV62 = SY102 ) )
| ~ ~ ( ~ ! [SY103: $i] :
( ( SV62 != SY103 )
| ! [SY104: $i] : ( member @ SV62 @ ( unordered_pair @ SY103 @ SY104 ) ) )
| ~ ! [SY105: $i,SY106: $i] :
( ( SV62 != SY106 )
| ( member @ SV62 @ ( unordered_pair @ SY105 @ SY106 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[323]) ).
thf(338,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK6_X @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( member @ ( sK6_X @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[324]) ).
thf(339,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[324]) ).
thf(340,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK4_Y @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( member @ SX0 @ ( sK4_Y @ SX1 @ SX0 ) ) )
| ( member @ SX0 @ ( product @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[325]) ).
thf(341,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( product @ SX1 ) )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( member @ SX0 @ SX2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[325]) ).
thf(342,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( equal_set @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[326]) ).
thf(343,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[326]) ).
thf(344,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( power_set @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[327]) ).
thf(345,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( member @ SX0 @ ( power_set @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[327]) ).
thf(346,plain,
! [SV63: $i] :
( ( ~ ! [SY107: $i,SY108: $i] :
( ~ ( member @ SV63 @ ( union @ SY107 @ SY108 ) )
| ( member @ SV63 @ SY107 )
| ( member @ SV63 @ SY108 ) )
| ~ ~ ( ~ ! [SY109: $i] :
( ~ ( member @ SV63 @ SY109 )
| ! [SY110: $i] : ( member @ SV63 @ ( union @ SY109 @ SY110 ) ) )
| ~ ! [SY111: $i,SY112: $i] :
( ~ ( member @ SV63 @ SY112 )
| ( member @ SV63 @ ( union @ SY111 @ SY112 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[328]) ).
thf(347,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ~ ( member @ SX0 @ SX2 ) )
| ( member @ SX0 @ ( sum @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[329]) ).
thf(348,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( sum @ SX1 ) )
| ~ ( ~ ( member @ ( sK5_Y @ SX1 @ SX0 ) @ SX1 )
| ~ ( member @ SX0 @ ( sK5_Y @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[329]) ).
thf(349,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( member @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[331]) ).
thf(350,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[332]) ).
thf(351,plain,
! [SV60: $i] :
( ( ~ ! [SY89: $i,SY90: $i] :
( ~ ( member @ SV60 @ SY90 )
| ( member @ SV60 @ SY89 )
| ( member @ SV60 @ ( difference @ SY90 @ SY89 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[333]) ).
thf(352,plain,
! [SV60: $i] :
( ( ~ ~ ( ~ ! [SY91: $i,SY92: $i] :
( ~ ( member @ SV60 @ ( difference @ SY92 @ SY91 ) )
| ( member @ SV60 @ SY92 ) )
| ~ ! [SY93: $i] :
( ! [SY94: $i] :
~ ( member @ SV60 @ ( difference @ SY94 @ SY93 ) )
| ~ ( member @ SV60 @ SY93 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[333]) ).
thf(353,plain,
! [SV61: $i] :
( ( ~ ! [SY95: $i,SY96: $i] :
( ~ ( member @ SV61 @ SY95 )
| ~ ( member @ SV61 @ SY96 )
| ( member @ SV61 @ ( intersection @ SY95 @ SY96 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[334]) ).
thf(354,plain,
! [SV61: $i] :
( ( ~ ~ ( ~ ! [SY97: $i] :
( ! [SY98: $i] :
~ ( member @ SV61 @ ( intersection @ SY97 @ SY98 ) )
| ( member @ SV61 @ SY97 ) )
| ~ ! [SY99: $i,SY100: $i] :
( ~ ( member @ SV61 @ ( intersection @ SY99 @ SY100 ) )
| ( member @ SV61 @ SY100 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[334]) ).
thf(355,plain,
( ( subset @ ( intersection @ sK1_A @ ( difference @ sK3_SY33 @ sK2_SY31 ) ) @ sK2_SY31 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[335]) ).
thf(356,plain,
( ( ~ ( subset @ sK1_A @ sK2_SY31 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[336]) ).
thf(357,plain,
! [SV62: $i] :
( ( ~ ! [SY101: $i,SY102: $i] :
( ~ ( member @ SV62 @ ( unordered_pair @ SY101 @ SY102 ) )
| ( SV62 = SY101 )
| ( SV62 = SY102 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[337]) ).
thf(358,plain,
! [SV62: $i] :
( ( ~ ~ ( ~ ! [SY103: $i] :
( ( SV62 != SY103 )
| ! [SY104: $i] : ( member @ SV62 @ ( unordered_pair @ SY103 @ SY104 ) ) )
| ~ ! [SY105: $i,SY106: $i] :
( ( SV62 != SY106 )
| ( member @ SV62 @ ( unordered_pair @ SY105 @ SY106 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[337]) ).
thf(359,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK6_X @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( member @ ( sK6_X @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[338]) ).
thf(360,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[339]) ).
thf(361,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK4_Y @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( member @ SX0 @ ( sK4_Y @ SX1 @ SX0 ) ) )
| ( member @ SX0 @ ( product @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[340]) ).
thf(362,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( product @ SX1 ) )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( member @ SX0 @ SX2 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[341]) ).
thf(363,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( equal_set @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[342]) ).
thf(364,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[343]) ).
thf(365,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( power_set @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[344]) ).
thf(366,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( member @ SX0 @ ( power_set @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[345]) ).
thf(367,plain,
! [SV63: $i] :
( ( ~ ! [SY107: $i,SY108: $i] :
( ~ ( member @ SV63 @ ( union @ SY107 @ SY108 ) )
| ( member @ SV63 @ SY107 )
| ( member @ SV63 @ SY108 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[346]) ).
thf(368,plain,
! [SV63: $i] :
( ( ~ ~ ( ~ ! [SY109: $i] :
( ~ ( member @ SV63 @ SY109 )
| ! [SY110: $i] : ( member @ SV63 @ ( union @ SY109 @ SY110 ) ) )
| ~ ! [SY111: $i,SY112: $i] :
( ~ ( member @ SV63 @ SY112 )
| ( member @ SV63 @ ( union @ SY111 @ SY112 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[346]) ).
thf(369,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ~ ( member @ SX0 @ SX2 ) )
| ( member @ SX0 @ ( sum @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[347]) ).
thf(370,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( sum @ SX1 ) )
| ~ ( ~ ( member @ ( sK5_Y @ SX1 @ SX0 ) @ SX1 )
| ~ ( member @ SX0 @ ( sK5_Y @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[348]) ).
thf(371,plain,
! [SV64: $i] :
( ( ! [SY113: $i] :
( ( SV64 != SY113 )
| ( member @ SV64 @ ( singleton @ SY113 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[349]) ).
thf(372,plain,
! [SV65: $i] :
( ( ! [SY114: $i] :
( ~ ( member @ SV65 @ ( singleton @ SY114 ) )
| ( SV65 = SY114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[350]) ).
thf(373,plain,
! [SV60: $i] :
( ( ! [SY89: $i,SY90: $i] :
( ~ ( member @ SV60 @ SY90 )
| ( member @ SV60 @ SY89 )
| ( member @ SV60 @ ( difference @ SY90 @ SY89 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[351]) ).
thf(374,plain,
! [SV60: $i] :
( ( ~ ( ~ ! [SY91: $i,SY92: $i] :
( ~ ( member @ SV60 @ ( difference @ SY92 @ SY91 ) )
| ( member @ SV60 @ SY92 ) )
| ~ ! [SY93: $i] :
( ! [SY94: $i] :
~ ( member @ SV60 @ ( difference @ SY94 @ SY93 ) )
| ~ ( member @ SV60 @ SY93 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[352]) ).
thf(375,plain,
! [SV61: $i] :
( ( ! [SY95: $i,SY96: $i] :
( ~ ( member @ SV61 @ SY95 )
| ~ ( member @ SV61 @ SY96 )
| ( member @ SV61 @ ( intersection @ SY95 @ SY96 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[353]) ).
thf(376,plain,
! [SV61: $i] :
( ( ~ ( ~ ! [SY97: $i] :
( ! [SY98: $i] :
~ ( member @ SV61 @ ( intersection @ SY97 @ SY98 ) )
| ( member @ SV61 @ SY97 ) )
| ~ ! [SY99: $i,SY100: $i] :
( ~ ( member @ SV61 @ ( intersection @ SY99 @ SY100 ) )
| ( member @ SV61 @ SY100 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[354]) ).
thf(377,plain,
( ( subset @ sK1_A @ sK2_SY31 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[356]) ).
thf(378,plain,
! [SV62: $i] :
( ( ! [SY101: $i,SY102: $i] :
( ~ ( member @ SV62 @ ( unordered_pair @ SY101 @ SY102 ) )
| ( SV62 = SY101 )
| ( SV62 = SY102 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[357]) ).
thf(379,plain,
! [SV62: $i] :
( ( ~ ( ~ ! [SY103: $i] :
( ( SV62 != SY103 )
| ! [SY104: $i] : ( member @ SV62 @ ( unordered_pair @ SY103 @ SY104 ) ) )
| ~ ! [SY105: $i,SY106: $i] :
( ( SV62 != SY106 )
| ( member @ SV62 @ ( unordered_pair @ SY105 @ SY106 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[358]) ).
thf(380,plain,
! [SV66: $i] :
( ( ! [SY115: $i] :
( ~ ( ~ ( member @ ( sK6_X @ SY115 @ SV66 ) @ SV66 )
| ~ ~ ( member @ ( sK6_X @ SY115 @ SV66 ) @ SY115 ) )
| ( subset @ SV66 @ SY115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[359]) ).
thf(381,plain,
! [SV67: $i] :
( ( ! [SY116: $i] :
( ~ ( subset @ SV67 @ SY116 )
| ! [SY117: $i] :
( ~ ( member @ SY117 @ SV67 )
| ( member @ SY117 @ SY116 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[360]) ).
thf(382,plain,
! [SV68: $i] :
( ( ! [SY118: $i] :
( ~ ( ~ ( member @ ( sK4_Y @ SY118 @ SV68 ) @ SY118 )
| ~ ~ ( member @ SV68 @ ( sK4_Y @ SY118 @ SV68 ) ) )
| ( member @ SV68 @ ( product @ SY118 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[361]) ).
thf(383,plain,
! [SV69: $i] :
( ( ! [SY119: $i] :
( ~ ( member @ SV69 @ ( product @ SY119 ) )
| ! [SY120: $i] :
( ~ ( member @ SY120 @ SY119 )
| ( member @ SV69 @ SY120 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[362]) ).
thf(384,plain,
! [SV70: $i] :
( ( ! [SY121: $i] :
( ~ ( subset @ SV70 @ SY121 )
| ~ ( subset @ SY121 @ SV70 )
| ( equal_set @ SV70 @ SY121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[363]) ).
thf(385,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[364]) ).
thf(386,plain,
! [SV71: $i] :
( ( ! [SY122: $i] :
( ~ ( member @ SV71 @ ( power_set @ SY122 ) )
| ( subset @ SV71 @ SY122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[365]) ).
thf(387,plain,
! [SV72: $i] :
( ( ! [SY123: $i] :
( ~ ( subset @ SV72 @ SY123 )
| ( member @ SV72 @ ( power_set @ SY123 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[366]) ).
thf(388,plain,
! [SV63: $i] :
( ( ! [SY107: $i,SY108: $i] :
( ~ ( member @ SV63 @ ( union @ SY107 @ SY108 ) )
| ( member @ SV63 @ SY107 )
| ( member @ SV63 @ SY108 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[367]) ).
thf(389,plain,
! [SV63: $i] :
( ( ~ ( ~ ! [SY109: $i] :
( ~ ( member @ SV63 @ SY109 )
| ! [SY110: $i] : ( member @ SV63 @ ( union @ SY109 @ SY110 ) ) )
| ~ ! [SY111: $i,SY112: $i] :
( ~ ( member @ SV63 @ SY112 )
| ( member @ SV63 @ ( union @ SY111 @ SY112 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[368]) ).
thf(390,plain,
! [SV73: $i] :
( ( ! [SY124: $i] :
( ! [SY125: $i] :
( ~ ( member @ SY125 @ SY124 )
| ~ ( member @ SV73 @ SY125 ) )
| ( member @ SV73 @ ( sum @ SY124 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[369]) ).
thf(391,plain,
! [SV74: $i] :
( ( ! [SY126: $i] :
( ~ ( member @ SV74 @ ( sum @ SY126 ) )
| ~ ( ~ ( member @ ( sK5_Y @ SY126 @ SV74 ) @ SY126 )
| ~ ( member @ SV74 @ ( sK5_Y @ SY126 @ SV74 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[370]) ).
thf(392,plain,
! [SV75: $i,SV64: $i] :
( ( ( SV64 != SV75 )
| ( member @ SV64 @ ( singleton @ SV75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[371]) ).
thf(393,plain,
! [SV76: $i,SV65: $i] :
( ( ~ ( member @ SV65 @ ( singleton @ SV76 ) )
| ( SV65 = SV76 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[372]) ).
thf(394,plain,
! [SV77: $i,SV60: $i] :
( ( ! [SY127: $i] :
( ~ ( member @ SV60 @ SY127 )
| ( member @ SV60 @ SV77 )
| ( member @ SV60 @ ( difference @ SY127 @ SV77 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[373]) ).
thf(395,plain,
! [SV60: $i] :
( ( ~ ! [SY91: $i,SY92: $i] :
( ~ ( member @ SV60 @ ( difference @ SY92 @ SY91 ) )
| ( member @ SV60 @ SY92 ) )
| ~ ! [SY93: $i] :
( ! [SY94: $i] :
~ ( member @ SV60 @ ( difference @ SY94 @ SY93 ) )
| ~ ( member @ SV60 @ SY93 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[374]) ).
thf(396,plain,
! [SV78: $i,SV61: $i] :
( ( ! [SY128: $i] :
( ~ ( member @ SV61 @ SV78 )
| ~ ( member @ SV61 @ SY128 )
| ( member @ SV61 @ ( intersection @ SV78 @ SY128 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[375]) ).
thf(397,plain,
! [SV61: $i] :
( ( ~ ! [SY97: $i] :
( ! [SY98: $i] :
~ ( member @ SV61 @ ( intersection @ SY97 @ SY98 ) )
| ( member @ SV61 @ SY97 ) )
| ~ ! [SY99: $i,SY100: $i] :
( ~ ( member @ SV61 @ ( intersection @ SY99 @ SY100 ) )
| ( member @ SV61 @ SY100 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[376]) ).
thf(398,plain,
! [SV79: $i,SV62: $i] :
( ( ! [SY129: $i] :
( ~ ( member @ SV62 @ ( unordered_pair @ SV79 @ SY129 ) )
| ( SV62 = SV79 )
| ( SV62 = SY129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[378]) ).
thf(399,plain,
! [SV62: $i] :
( ( ~ ! [SY103: $i] :
( ( SV62 != SY103 )
| ! [SY104: $i] : ( member @ SV62 @ ( unordered_pair @ SY103 @ SY104 ) ) )
| ~ ! [SY105: $i,SY106: $i] :
( ( SV62 != SY106 )
| ( member @ SV62 @ ( unordered_pair @ SY105 @ SY106 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[379]) ).
thf(400,plain,
! [SV66: $i,SV80: $i] :
( ( ~ ( ~ ( member @ ( sK6_X @ SV80 @ SV66 ) @ SV66 )
| ~ ~ ( member @ ( sK6_X @ SV80 @ SV66 ) @ SV80 ) )
| ( subset @ SV66 @ SV80 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[380]) ).
thf(401,plain,
! [SV81: $i,SV67: $i] :
( ( ~ ( subset @ SV67 @ SV81 )
| ! [SY130: $i] :
( ~ ( member @ SY130 @ SV67 )
| ( member @ SY130 @ SV81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[381]) ).
thf(402,plain,
! [SV68: $i,SV82: $i] :
( ( ~ ( ~ ( member @ ( sK4_Y @ SV82 @ SV68 ) @ SV82 )
| ~ ~ ( member @ SV68 @ ( sK4_Y @ SV82 @ SV68 ) ) )
| ( member @ SV68 @ ( product @ SV82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[382]) ).
thf(403,plain,
! [SV83: $i,SV69: $i] :
( ( ~ ( member @ SV69 @ ( product @ SV83 ) )
| ! [SY131: $i] :
( ~ ( member @ SY131 @ SV83 )
| ( member @ SV69 @ SY131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[383]) ).
thf(404,plain,
! [SV84: $i,SV70: $i] :
( ( ~ ( subset @ SV70 @ SV84 )
| ~ ( subset @ SV84 @ SV70 )
| ( equal_set @ SV70 @ SV84 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[384]) ).
thf(405,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[385]) ).
thf(406,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[385]) ).
thf(407,plain,
! [SV85: $i,SV71: $i] :
( ( ~ ( member @ SV71 @ ( power_set @ SV85 ) )
| ( subset @ SV71 @ SV85 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[386]) ).
thf(408,plain,
! [SV86: $i,SV72: $i] :
( ( ~ ( subset @ SV72 @ SV86 )
| ( member @ SV72 @ ( power_set @ SV86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[387]) ).
thf(409,plain,
! [SV87: $i,SV63: $i] :
( ( ! [SY132: $i] :
( ~ ( member @ SV63 @ ( union @ SV87 @ SY132 ) )
| ( member @ SV63 @ SV87 )
| ( member @ SV63 @ SY132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[388]) ).
thf(410,plain,
! [SV63: $i] :
( ( ~ ! [SY109: $i] :
( ~ ( member @ SV63 @ SY109 )
| ! [SY110: $i] : ( member @ SV63 @ ( union @ SY109 @ SY110 ) ) )
| ~ ! [SY111: $i,SY112: $i] :
( ~ ( member @ SV63 @ SY112 )
| ( member @ SV63 @ ( union @ SY111 @ SY112 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[389]) ).
thf(411,plain,
! [SV73: $i,SV88: $i] :
( ( ! [SY133: $i] :
( ~ ( member @ SY133 @ SV88 )
| ~ ( member @ SV73 @ SY133 ) )
| ( member @ SV73 @ ( sum @ SV88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[390]) ).
thf(412,plain,
! [SV89: $i,SV74: $i] :
( ( ~ ( member @ SV74 @ ( sum @ SV89 ) )
| ~ ( ~ ( member @ ( sK5_Y @ SV89 @ SV74 ) @ SV89 )
| ~ ( member @ SV74 @ ( sK5_Y @ SV89 @ SV74 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[391]) ).
thf(413,plain,
! [SV75: $i,SV64: $i] :
( ( ( ( SV64 != SV75 ) )
= $true )
| ( ( member @ SV64 @ ( singleton @ SV75 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[392]) ).
thf(414,plain,
! [SV76: $i,SV65: $i] :
( ( ( ~ ( member @ SV65 @ ( singleton @ SV76 ) ) )
= $true )
| ( ( SV65 = SV76 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[393]) ).
thf(415,plain,
! [SV77: $i,SV90: $i,SV60: $i] :
( ( ~ ( member @ SV60 @ SV90 )
| ( member @ SV60 @ SV77 )
| ( member @ SV60 @ ( difference @ SV90 @ SV77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[394]) ).
thf(416,plain,
! [SV60: $i] :
( ( ~ ! [SY91: $i,SY92: $i] :
( ~ ( member @ SV60 @ ( difference @ SY92 @ SY91 ) )
| ( member @ SV60 @ SY92 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[395]) ).
thf(417,plain,
! [SV60: $i] :
( ( ~ ! [SY93: $i] :
( ! [SY94: $i] :
~ ( member @ SV60 @ ( difference @ SY94 @ SY93 ) )
| ~ ( member @ SV60 @ SY93 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[395]) ).
thf(418,plain,
! [SV91: $i,SV78: $i,SV61: $i] :
( ( ~ ( member @ SV61 @ SV78 )
| ~ ( member @ SV61 @ SV91 )
| ( member @ SV61 @ ( intersection @ SV78 @ SV91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[396]) ).
thf(419,plain,
! [SV61: $i] :
( ( ~ ! [SY97: $i] :
( ! [SY98: $i] :
~ ( member @ SV61 @ ( intersection @ SY97 @ SY98 ) )
| ( member @ SV61 @ SY97 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[397]) ).
thf(420,plain,
! [SV61: $i] :
( ( ~ ! [SY99: $i,SY100: $i] :
( ~ ( member @ SV61 @ ( intersection @ SY99 @ SY100 ) )
| ( member @ SV61 @ SY100 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[397]) ).
thf(421,plain,
! [SV92: $i,SV79: $i,SV62: $i] :
( ( ~ ( member @ SV62 @ ( unordered_pair @ SV79 @ SV92 ) )
| ( SV62 = SV79 )
| ( SV62 = SV92 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[398]) ).
thf(422,plain,
! [SV62: $i] :
( ( ~ ! [SY103: $i] :
( ( SV62 != SY103 )
| ! [SY104: $i] : ( member @ SV62 @ ( unordered_pair @ SY103 @ SY104 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[399]) ).
thf(423,plain,
! [SV62: $i] :
( ( ~ ! [SY105: $i,SY106: $i] :
( ( SV62 != SY106 )
| ( member @ SV62 @ ( unordered_pair @ SY105 @ SY106 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[399]) ).
thf(424,plain,
! [SV66: $i,SV80: $i] :
( ( ( ~ ( ~ ( member @ ( sK6_X @ SV80 @ SV66 ) @ SV66 )
| ~ ~ ( member @ ( sK6_X @ SV80 @ SV66 ) @ SV80 ) ) )
= $true )
| ( ( subset @ SV66 @ SV80 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[400]) ).
thf(425,plain,
! [SV81: $i,SV67: $i] :
( ( ( ~ ( subset @ SV67 @ SV81 ) )
= $true )
| ( ( ! [SY130: $i] :
( ~ ( member @ SY130 @ SV67 )
| ( member @ SY130 @ SV81 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[401]) ).
thf(426,plain,
! [SV68: $i,SV82: $i] :
( ( ( ~ ( ~ ( member @ ( sK4_Y @ SV82 @ SV68 ) @ SV82 )
| ~ ~ ( member @ SV68 @ ( sK4_Y @ SV82 @ SV68 ) ) ) )
= $true )
| ( ( member @ SV68 @ ( product @ SV82 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[402]) ).
thf(427,plain,
! [SV83: $i,SV69: $i] :
( ( ( ~ ( member @ SV69 @ ( product @ SV83 ) ) )
= $true )
| ( ( ! [SY131: $i] :
( ~ ( member @ SY131 @ SV83 )
| ( member @ SV69 @ SY131 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[403]) ).
thf(428,plain,
! [SV84: $i,SV70: $i] :
( ( ( ~ ( subset @ SV70 @ SV84 )
| ~ ( subset @ SV84 @ SV70 ) )
= $true )
| ( ( equal_set @ SV70 @ SV84 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[404]) ).
thf(429,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[405]) ).
thf(430,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[406]) ).
thf(431,plain,
! [SV85: $i,SV71: $i] :
( ( ( ~ ( member @ SV71 @ ( power_set @ SV85 ) ) )
= $true )
| ( ( subset @ SV71 @ SV85 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[407]) ).
thf(432,plain,
! [SV86: $i,SV72: $i] :
( ( ( ~ ( subset @ SV72 @ SV86 ) )
= $true )
| ( ( member @ SV72 @ ( power_set @ SV86 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[408]) ).
thf(433,plain,
! [SV93: $i,SV87: $i,SV63: $i] :
( ( ~ ( member @ SV63 @ ( union @ SV87 @ SV93 ) )
| ( member @ SV63 @ SV87 )
| ( member @ SV63 @ SV93 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[409]) ).
thf(434,plain,
! [SV63: $i] :
( ( ~ ! [SY109: $i] :
( ~ ( member @ SV63 @ SY109 )
| ! [SY110: $i] : ( member @ SV63 @ ( union @ SY109 @ SY110 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[410]) ).
thf(435,plain,
! [SV63: $i] :
( ( ~ ! [SY111: $i,SY112: $i] :
( ~ ( member @ SV63 @ SY112 )
| ( member @ SV63 @ ( union @ SY111 @ SY112 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[410]) ).
thf(436,plain,
! [SV73: $i,SV88: $i] :
( ( ( ! [SY133: $i] :
( ~ ( member @ SY133 @ SV88 )
| ~ ( member @ SV73 @ SY133 ) ) )
= $true )
| ( ( member @ SV73 @ ( sum @ SV88 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[411]) ).
thf(437,plain,
! [SV89: $i,SV74: $i] :
( ( ( ~ ( member @ SV74 @ ( sum @ SV89 ) ) )
= $true )
| ( ( ~ ( ~ ( member @ ( sK5_Y @ SV89 @ SV74 ) @ SV89 )
| ~ ( member @ SV74 @ ( sK5_Y @ SV89 @ SV74 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[412]) ).
thf(438,plain,
! [SV75: $i,SV64: $i] :
( ( ( SV64 = SV75 )
= $false )
| ( ( member @ SV64 @ ( singleton @ SV75 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[413]) ).
thf(439,plain,
! [SV76: $i,SV65: $i] :
( ( ( member @ SV65 @ ( singleton @ SV76 ) )
= $false )
| ( ( SV65 = SV76 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[414]) ).
thf(440,plain,
! [SV77: $i,SV90: $i,SV60: $i] :
( ( ( ~ ( member @ SV60 @ SV90 )
| ( member @ SV60 @ SV77 ) )
= $true )
| ( ( member @ SV60 @ ( difference @ SV90 @ SV77 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[415]) ).
thf(441,plain,
! [SV60: $i] :
( ( ! [SY91: $i,SY92: $i] :
( ~ ( member @ SV60 @ ( difference @ SY92 @ SY91 ) )
| ( member @ SV60 @ SY92 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[416]) ).
thf(442,plain,
! [SV60: $i] :
( ( ! [SY93: $i] :
( ! [SY94: $i] :
~ ( member @ SV60 @ ( difference @ SY94 @ SY93 ) )
| ~ ( member @ SV60 @ SY93 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[417]) ).
thf(443,plain,
! [SV91: $i,SV78: $i,SV61: $i] :
( ( ( ~ ( member @ SV61 @ SV78 )
| ~ ( member @ SV61 @ SV91 ) )
= $true )
| ( ( member @ SV61 @ ( intersection @ SV78 @ SV91 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[418]) ).
thf(444,plain,
! [SV61: $i] :
( ( ! [SY97: $i] :
( ! [SY98: $i] :
~ ( member @ SV61 @ ( intersection @ SY97 @ SY98 ) )
| ( member @ SV61 @ SY97 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[419]) ).
thf(445,plain,
! [SV61: $i] :
( ( ! [SY99: $i,SY100: $i] :
( ~ ( member @ SV61 @ ( intersection @ SY99 @ SY100 ) )
| ( member @ SV61 @ SY100 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[420]) ).
thf(446,plain,
! [SV92: $i,SV79: $i,SV62: $i] :
( ( ( ~ ( member @ SV62 @ ( unordered_pair @ SV79 @ SV92 ) ) )
= $true )
| ( ( ( SV62 = SV79 )
| ( SV62 = SV92 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[421]) ).
thf(447,plain,
! [SV62: $i] :
( ( ! [SY103: $i] :
( ( SV62 != SY103 )
| ! [SY104: $i] : ( member @ SV62 @ ( unordered_pair @ SY103 @ SY104 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[422]) ).
thf(448,plain,
! [SV62: $i] :
( ( ! [SY105: $i,SY106: $i] :
( ( SV62 != SY106 )
| ( member @ SV62 @ ( unordered_pair @ SY105 @ SY106 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[423]) ).
thf(449,plain,
! [SV66: $i,SV80: $i] :
( ( ( ~ ( member @ ( sK6_X @ SV80 @ SV66 ) @ SV66 )
| ~ ~ ( member @ ( sK6_X @ SV80 @ SV66 ) @ SV80 ) )
= $false )
| ( ( subset @ SV66 @ SV80 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[424]) ).
thf(450,plain,
! [SV81: $i,SV67: $i] :
( ( ( subset @ SV67 @ SV81 )
= $false )
| ( ( ! [SY130: $i] :
( ~ ( member @ SY130 @ SV67 )
| ( member @ SY130 @ SV81 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[425]) ).
thf(451,plain,
! [SV68: $i,SV82: $i] :
( ( ( ~ ( member @ ( sK4_Y @ SV82 @ SV68 ) @ SV82 )
| ~ ~ ( member @ SV68 @ ( sK4_Y @ SV82 @ SV68 ) ) )
= $false )
| ( ( member @ SV68 @ ( product @ SV82 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[426]) ).
thf(452,plain,
! [SV83: $i,SV69: $i] :
( ( ( member @ SV69 @ ( product @ SV83 ) )
= $false )
| ( ( ! [SY131: $i] :
( ~ ( member @ SY131 @ SV83 )
| ( member @ SV69 @ SY131 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[427]) ).
thf(453,plain,
! [SV84: $i,SV70: $i] :
( ( ( ~ ( subset @ SV70 @ SV84 ) )
= $true )
| ( ( ~ ( subset @ SV84 @ SV70 ) )
= $true )
| ( ( equal_set @ SV70 @ SV84 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[428]) ).
thf(454,plain,
! [SV94: $i] :
( ( ! [SY134: $i] :
( ~ ( equal_set @ SV94 @ SY134 )
| ( subset @ SV94 @ SY134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[429]) ).
thf(455,plain,
! [SV95: $i] :
( ( ! [SY135: $i] :
( ~ ( equal_set @ SV95 @ SY135 )
| ( subset @ SY135 @ SV95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[430]) ).
thf(456,plain,
! [SV85: $i,SV71: $i] :
( ( ( member @ SV71 @ ( power_set @ SV85 ) )
= $false )
| ( ( subset @ SV71 @ SV85 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[431]) ).
thf(457,plain,
! [SV86: $i,SV72: $i] :
( ( ( subset @ SV72 @ SV86 )
= $false )
| ( ( member @ SV72 @ ( power_set @ SV86 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[432]) ).
thf(458,plain,
! [SV93: $i,SV87: $i,SV63: $i] :
( ( ( ~ ( member @ SV63 @ ( union @ SV87 @ SV93 ) ) )
= $true )
| ( ( ( member @ SV63 @ SV87 )
| ( member @ SV63 @ SV93 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[433]) ).
thf(459,plain,
! [SV63: $i] :
( ( ! [SY109: $i] :
( ~ ( member @ SV63 @ SY109 )
| ! [SY110: $i] : ( member @ SV63 @ ( union @ SY109 @ SY110 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[434]) ).
thf(460,plain,
! [SV63: $i] :
( ( ! [SY111: $i,SY112: $i] :
( ~ ( member @ SV63 @ SY112 )
| ( member @ SV63 @ ( union @ SY111 @ SY112 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[435]) ).
thf(461,plain,
! [SV73: $i,SV88: $i,SV96: $i] :
( ( ( ~ ( member @ SV96 @ SV88 )
| ~ ( member @ SV73 @ SV96 ) )
= $true )
| ( ( member @ SV73 @ ( sum @ SV88 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[436]) ).
thf(462,plain,
! [SV89: $i,SV74: $i] :
( ( ( member @ SV74 @ ( sum @ SV89 ) )
= $false )
| ( ( ~ ( ~ ( member @ ( sK5_Y @ SV89 @ SV74 ) @ SV89 )
| ~ ( member @ SV74 @ ( sK5_Y @ SV89 @ SV74 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[437]) ).
thf(463,plain,
! [SV77: $i,SV90: $i,SV60: $i] :
( ( ( ~ ( member @ SV60 @ SV90 ) )
= $true )
| ( ( member @ SV60 @ SV77 )
= $true )
| ( ( member @ SV60 @ ( difference @ SV90 @ SV77 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[440]) ).
thf(464,plain,
! [SV97: $i,SV60: $i] :
( ( ! [SY136: $i] :
( ~ ( member @ SV60 @ ( difference @ SY136 @ SV97 ) )
| ( member @ SV60 @ SY136 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[441]) ).
thf(465,plain,
! [SV98: $i,SV60: $i] :
( ( ! [SY137: $i] :
~ ( member @ SV60 @ ( difference @ SY137 @ SV98 ) )
| ~ ( member @ SV60 @ SV98 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[442]) ).
thf(466,plain,
! [SV91: $i,SV78: $i,SV61: $i] :
( ( ( ~ ( member @ SV61 @ SV78 ) )
= $true )
| ( ( ~ ( member @ SV61 @ SV91 ) )
= $true )
| ( ( member @ SV61 @ ( intersection @ SV78 @ SV91 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[443]) ).
thf(467,plain,
! [SV99: $i,SV61: $i] :
( ( ! [SY138: $i] :
~ ( member @ SV61 @ ( intersection @ SV99 @ SY138 ) )
| ( member @ SV61 @ SV99 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[444]) ).
thf(468,plain,
! [SV100: $i,SV61: $i] :
( ( ! [SY139: $i] :
( ~ ( member @ SV61 @ ( intersection @ SV100 @ SY139 ) )
| ( member @ SV61 @ SY139 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[445]) ).
thf(469,plain,
! [SV92: $i,SV79: $i,SV62: $i] :
( ( ( member @ SV62 @ ( unordered_pair @ SV79 @ SV92 ) )
= $false )
| ( ( ( SV62 = SV79 )
| ( SV62 = SV92 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[446]) ).
thf(470,plain,
! [SV101: $i,SV62: $i] :
( ( ( SV62 != SV101 )
| ! [SY140: $i] : ( member @ SV62 @ ( unordered_pair @ SV101 @ SY140 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[447]) ).
thf(471,plain,
! [SV102: $i,SV62: $i] :
( ( ! [SY141: $i] :
( ( SV62 != SY141 )
| ( member @ SV62 @ ( unordered_pair @ SV102 @ SY141 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[448]) ).
thf(472,plain,
! [SV66: $i,SV80: $i] :
( ( ( ~ ( member @ ( sK6_X @ SV80 @ SV66 ) @ SV66 ) )
= $false )
| ( ( subset @ SV66 @ SV80 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[449]) ).
thf(473,plain,
! [SV66: $i,SV80: $i] :
( ( ( ~ ~ ( member @ ( sK6_X @ SV80 @ SV66 ) @ SV80 ) )
= $false )
| ( ( subset @ SV66 @ SV80 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[449]) ).
thf(474,plain,
! [SV81: $i,SV67: $i,SV103: $i] :
( ( ( ~ ( member @ SV103 @ SV67 )
| ( member @ SV103 @ SV81 ) )
= $true )
| ( ( subset @ SV67 @ SV81 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[450]) ).
thf(475,plain,
! [SV68: $i,SV82: $i] :
( ( ( ~ ( member @ ( sK4_Y @ SV82 @ SV68 ) @ SV82 ) )
= $false )
| ( ( member @ SV68 @ ( product @ SV82 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[451]) ).
thf(476,plain,
! [SV82: $i,SV68: $i] :
( ( ( ~ ~ ( member @ SV68 @ ( sK4_Y @ SV82 @ SV68 ) ) )
= $false )
| ( ( member @ SV68 @ ( product @ SV82 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[451]) ).
thf(477,plain,
! [SV69: $i,SV83: $i,SV104: $i] :
( ( ( ~ ( member @ SV104 @ SV83 )
| ( member @ SV69 @ SV104 ) )
= $true )
| ( ( member @ SV69 @ ( product @ SV83 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[452]) ).
thf(478,plain,
! [SV84: $i,SV70: $i] :
( ( ( subset @ SV70 @ SV84 )
= $false )
| ( ( ~ ( subset @ SV84 @ SV70 ) )
= $true )
| ( ( equal_set @ SV70 @ SV84 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[453]) ).
thf(479,plain,
! [SV105: $i,SV94: $i] :
( ( ~ ( equal_set @ SV94 @ SV105 )
| ( subset @ SV94 @ SV105 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[454]) ).
thf(480,plain,
! [SV106: $i,SV95: $i] :
( ( ~ ( equal_set @ SV95 @ SV106 )
| ( subset @ SV106 @ SV95 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[455]) ).
thf(481,plain,
! [SV93: $i,SV87: $i,SV63: $i] :
( ( ( member @ SV63 @ ( union @ SV87 @ SV93 ) )
= $false )
| ( ( ( member @ SV63 @ SV87 )
| ( member @ SV63 @ SV93 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[458]) ).
thf(482,plain,
! [SV107: $i,SV63: $i] :
( ( ~ ( member @ SV63 @ SV107 )
| ! [SY142: $i] : ( member @ SV63 @ ( union @ SV107 @ SY142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[459]) ).
thf(483,plain,
! [SV108: $i,SV63: $i] :
( ( ! [SY143: $i] :
( ~ ( member @ SV63 @ SY143 )
| ( member @ SV63 @ ( union @ SV108 @ SY143 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[460]) ).
thf(484,plain,
! [SV73: $i,SV88: $i,SV96: $i] :
( ( ( ~ ( member @ SV96 @ SV88 ) )
= $true )
| ( ( ~ ( member @ SV73 @ SV96 ) )
= $true )
| ( ( member @ SV73 @ ( sum @ SV88 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[461]) ).
thf(485,plain,
! [SV74: $i,SV89: $i] :
( ( ( ~ ( member @ ( sK5_Y @ SV89 @ SV74 ) @ SV89 )
| ~ ( member @ SV74 @ ( sK5_Y @ SV89 @ SV74 ) ) )
= $false )
| ( ( member @ SV74 @ ( sum @ SV89 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[462]) ).
thf(486,plain,
! [SV77: $i,SV90: $i,SV60: $i] :
( ( ( member @ SV60 @ SV90 )
= $false )
| ( ( member @ SV60 @ SV77 )
= $true )
| ( ( member @ SV60 @ ( difference @ SV90 @ SV77 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[463]) ).
thf(487,plain,
! [SV97: $i,SV109: $i,SV60: $i] :
( ( ~ ( member @ SV60 @ ( difference @ SV109 @ SV97 ) )
| ( member @ SV60 @ SV109 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[464]) ).
thf(488,plain,
! [SV98: $i,SV60: $i] :
( ( ( ! [SY137: $i] :
~ ( member @ SV60 @ ( difference @ SY137 @ SV98 ) ) )
= $true )
| ( ( ~ ( member @ SV60 @ SV98 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[465]) ).
thf(489,plain,
! [SV91: $i,SV78: $i,SV61: $i] :
( ( ( member @ SV61 @ SV78 )
= $false )
| ( ( ~ ( member @ SV61 @ SV91 ) )
= $true )
| ( ( member @ SV61 @ ( intersection @ SV78 @ SV91 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[466]) ).
thf(490,plain,
! [SV99: $i,SV61: $i] :
( ( ( ! [SY138: $i] :
~ ( member @ SV61 @ ( intersection @ SV99 @ SY138 ) ) )
= $true )
| ( ( member @ SV61 @ SV99 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[467]) ).
thf(491,plain,
! [SV110: $i,SV100: $i,SV61: $i] :
( ( ~ ( member @ SV61 @ ( intersection @ SV100 @ SV110 ) )
| ( member @ SV61 @ SV110 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[468]) ).
thf(492,plain,
! [SV92: $i,SV79: $i,SV62: $i] :
( ( ( SV62 = SV79 )
= $true )
| ( ( SV62 = SV92 )
= $true )
| ( ( member @ SV62 @ ( unordered_pair @ SV79 @ SV92 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[469]) ).
thf(493,plain,
! [SV101: $i,SV62: $i] :
( ( ( ( SV62 != SV101 ) )
= $true )
| ( ( ! [SY140: $i] : ( member @ SV62 @ ( unordered_pair @ SV101 @ SY140 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[470]) ).
thf(494,plain,
! [SV102: $i,SV111: $i,SV62: $i] :
( ( ( SV62 != SV111 )
| ( member @ SV62 @ ( unordered_pair @ SV102 @ SV111 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[471]) ).
thf(495,plain,
! [SV66: $i,SV80: $i] :
( ( ( member @ ( sK6_X @ SV80 @ SV66 ) @ SV66 )
= $true )
| ( ( subset @ SV66 @ SV80 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[472]) ).
thf(496,plain,
! [SV66: $i,SV80: $i] :
( ( ( ~ ( member @ ( sK6_X @ SV80 @ SV66 ) @ SV80 ) )
= $true )
| ( ( subset @ SV66 @ SV80 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[473]) ).
thf(497,plain,
! [SV81: $i,SV67: $i,SV103: $i] :
( ( ( ~ ( member @ SV103 @ SV67 ) )
= $true )
| ( ( member @ SV103 @ SV81 )
= $true )
| ( ( subset @ SV67 @ SV81 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[474]) ).
thf(498,plain,
! [SV68: $i,SV82: $i] :
( ( ( member @ ( sK4_Y @ SV82 @ SV68 ) @ SV82 )
= $true )
| ( ( member @ SV68 @ ( product @ SV82 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[475]) ).
thf(499,plain,
! [SV82: $i,SV68: $i] :
( ( ( ~ ( member @ SV68 @ ( sK4_Y @ SV82 @ SV68 ) ) )
= $true )
| ( ( member @ SV68 @ ( product @ SV82 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[476]) ).
thf(500,plain,
! [SV69: $i,SV83: $i,SV104: $i] :
( ( ( ~ ( member @ SV104 @ SV83 ) )
= $true )
| ( ( member @ SV69 @ SV104 )
= $true )
| ( ( member @ SV69 @ ( product @ SV83 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[477]) ).
thf(501,plain,
! [SV70: $i,SV84: $i] :
( ( ( subset @ SV84 @ SV70 )
= $false )
| ( ( subset @ SV70 @ SV84 )
= $false )
| ( ( equal_set @ SV70 @ SV84 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[478]) ).
thf(502,plain,
! [SV105: $i,SV94: $i] :
( ( ( ~ ( equal_set @ SV94 @ SV105 ) )
= $true )
| ( ( subset @ SV94 @ SV105 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[479]) ).
thf(503,plain,
! [SV106: $i,SV95: $i] :
( ( ( ~ ( equal_set @ SV95 @ SV106 ) )
= $true )
| ( ( subset @ SV106 @ SV95 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[480]) ).
thf(504,plain,
! [SV93: $i,SV87: $i,SV63: $i] :
( ( ( member @ SV63 @ SV87 )
= $true )
| ( ( member @ SV63 @ SV93 )
= $true )
| ( ( member @ SV63 @ ( union @ SV87 @ SV93 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[481]) ).
thf(505,plain,
! [SV107: $i,SV63: $i] :
( ( ( ~ ( member @ SV63 @ SV107 ) )
= $true )
| ( ( ! [SY142: $i] : ( member @ SV63 @ ( union @ SV107 @ SY142 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[482]) ).
thf(506,plain,
! [SV108: $i,SV112: $i,SV63: $i] :
( ( ~ ( member @ SV63 @ SV112 )
| ( member @ SV63 @ ( union @ SV108 @ SV112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[483]) ).
thf(507,plain,
! [SV73: $i,SV88: $i,SV96: $i] :
( ( ( member @ SV96 @ SV88 )
= $false )
| ( ( ~ ( member @ SV73 @ SV96 ) )
= $true )
| ( ( member @ SV73 @ ( sum @ SV88 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[484]) ).
thf(508,plain,
! [SV74: $i,SV89: $i] :
( ( ( ~ ( member @ ( sK5_Y @ SV89 @ SV74 ) @ SV89 ) )
= $false )
| ( ( member @ SV74 @ ( sum @ SV89 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[485]) ).
thf(509,plain,
! [SV89: $i,SV74: $i] :
( ( ( ~ ( member @ SV74 @ ( sK5_Y @ SV89 @ SV74 ) ) )
= $false )
| ( ( member @ SV74 @ ( sum @ SV89 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[485]) ).
thf(510,plain,
! [SV97: $i,SV109: $i,SV60: $i] :
( ( ( ~ ( member @ SV60 @ ( difference @ SV109 @ SV97 ) ) )
= $true )
| ( ( member @ SV60 @ SV109 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[487]) ).
thf(511,plain,
! [SV98: $i,SV113: $i,SV60: $i] :
( ( ( ~ ( member @ SV60 @ ( difference @ SV113 @ SV98 ) ) )
= $true )
| ( ( ~ ( member @ SV60 @ SV98 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[488]) ).
thf(512,plain,
! [SV78: $i,SV91: $i,SV61: $i] :
( ( ( member @ SV61 @ SV91 )
= $false )
| ( ( member @ SV61 @ SV78 )
= $false )
| ( ( member @ SV61 @ ( intersection @ SV78 @ SV91 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[489]) ).
thf(513,plain,
! [SV114: $i,SV99: $i,SV61: $i] :
( ( ( ~ ( member @ SV61 @ ( intersection @ SV99 @ SV114 ) ) )
= $true )
| ( ( member @ SV61 @ SV99 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[490]) ).
thf(514,plain,
! [SV110: $i,SV100: $i,SV61: $i] :
( ( ( ~ ( member @ SV61 @ ( intersection @ SV100 @ SV110 ) ) )
= $true )
| ( ( member @ SV61 @ SV110 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[491]) ).
thf(515,plain,
! [SV101: $i,SV62: $i] :
( ( ( SV62 = SV101 )
= $false )
| ( ( ! [SY140: $i] : ( member @ SV62 @ ( unordered_pair @ SV101 @ SY140 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[493]) ).
thf(516,plain,
! [SV102: $i,SV111: $i,SV62: $i] :
( ( ( ( SV62 != SV111 ) )
= $true )
| ( ( member @ SV62 @ ( unordered_pair @ SV102 @ SV111 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[494]) ).
thf(517,plain,
! [SV66: $i,SV80: $i] :
( ( ( member @ ( sK6_X @ SV80 @ SV66 ) @ SV80 )
= $false )
| ( ( subset @ SV66 @ SV80 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[496]) ).
thf(518,plain,
! [SV81: $i,SV67: $i,SV103: $i] :
( ( ( member @ SV103 @ SV67 )
= $false )
| ( ( member @ SV103 @ SV81 )
= $true )
| ( ( subset @ SV67 @ SV81 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[497]) ).
thf(519,plain,
! [SV82: $i,SV68: $i] :
( ( ( member @ SV68 @ ( sK4_Y @ SV82 @ SV68 ) )
= $false )
| ( ( member @ SV68 @ ( product @ SV82 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[499]) ).
thf(520,plain,
! [SV69: $i,SV83: $i,SV104: $i] :
( ( ( member @ SV104 @ SV83 )
= $false )
| ( ( member @ SV69 @ SV104 )
= $true )
| ( ( member @ SV69 @ ( product @ SV83 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[500]) ).
thf(521,plain,
! [SV105: $i,SV94: $i] :
( ( ( equal_set @ SV94 @ SV105 )
= $false )
| ( ( subset @ SV94 @ SV105 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[502]) ).
thf(522,plain,
! [SV106: $i,SV95: $i] :
( ( ( equal_set @ SV95 @ SV106 )
= $false )
| ( ( subset @ SV106 @ SV95 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[503]) ).
thf(523,plain,
! [SV107: $i,SV63: $i] :
( ( ( member @ SV63 @ SV107 )
= $false )
| ( ( ! [SY142: $i] : ( member @ SV63 @ ( union @ SV107 @ SY142 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[505]) ).
thf(524,plain,
! [SV108: $i,SV112: $i,SV63: $i] :
( ( ( ~ ( member @ SV63 @ SV112 ) )
= $true )
| ( ( member @ SV63 @ ( union @ SV108 @ SV112 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[506]) ).
thf(525,plain,
! [SV88: $i,SV96: $i,SV73: $i] :
( ( ( member @ SV73 @ SV96 )
= $false )
| ( ( member @ SV96 @ SV88 )
= $false )
| ( ( member @ SV73 @ ( sum @ SV88 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[507]) ).
thf(526,plain,
! [SV74: $i,SV89: $i] :
( ( ( member @ ( sK5_Y @ SV89 @ SV74 ) @ SV89 )
= $true )
| ( ( member @ SV74 @ ( sum @ SV89 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[508]) ).
thf(527,plain,
! [SV89: $i,SV74: $i] :
( ( ( member @ SV74 @ ( sK5_Y @ SV89 @ SV74 ) )
= $true )
| ( ( member @ SV74 @ ( sum @ SV89 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[509]) ).
thf(528,plain,
! [SV97: $i,SV109: $i,SV60: $i] :
( ( ( member @ SV60 @ ( difference @ SV109 @ SV97 ) )
= $false )
| ( ( member @ SV60 @ SV109 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[510]) ).
thf(529,plain,
! [SV98: $i,SV113: $i,SV60: $i] :
( ( ( member @ SV60 @ ( difference @ SV113 @ SV98 ) )
= $false )
| ( ( ~ ( member @ SV60 @ SV98 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[511]) ).
thf(530,plain,
! [SV114: $i,SV99: $i,SV61: $i] :
( ( ( member @ SV61 @ ( intersection @ SV99 @ SV114 ) )
= $false )
| ( ( member @ SV61 @ SV99 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[513]) ).
thf(531,plain,
! [SV110: $i,SV100: $i,SV61: $i] :
( ( ( member @ SV61 @ ( intersection @ SV100 @ SV110 ) )
= $false )
| ( ( member @ SV61 @ SV110 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[514]) ).
thf(532,plain,
! [SV115: $i,SV101: $i,SV62: $i] :
( ( ( member @ SV62 @ ( unordered_pair @ SV101 @ SV115 ) )
= $true )
| ( ( SV62 = SV101 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[515]) ).
thf(533,plain,
! [SV102: $i,SV111: $i,SV62: $i] :
( ( ( SV62 = SV111 )
= $false )
| ( ( member @ SV62 @ ( unordered_pair @ SV102 @ SV111 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[516]) ).
thf(534,plain,
! [SV116: $i,SV107: $i,SV63: $i] :
( ( ( member @ SV63 @ ( union @ SV107 @ SV116 ) )
= $true )
| ( ( member @ SV63 @ SV107 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[523]) ).
thf(535,plain,
! [SV108: $i,SV112: $i,SV63: $i] :
( ( ( member @ SV63 @ SV112 )
= $false )
| ( ( member @ SV63 @ ( union @ SV108 @ SV112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[524]) ).
thf(536,plain,
! [SV113: $i,SV98: $i,SV60: $i] :
( ( ( member @ SV60 @ SV98 )
= $false )
| ( ( member @ SV60 @ ( difference @ SV113 @ SV98 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[529]) ).
thf(537,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[304,536,535,534,533,532,531,530,528,527,526,525,522,521,520,519,518,517,512,504,501,498,495,492,486,457,456,439,438,377,355,330,305]) ).
thf(538,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[537,292]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET700+4 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.35 % Computer : n010.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sun Jul 10 01:25:30 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36
% 0.13/0.36 No.of.Axioms: 11
% 0.13/0.36
% 0.13/0.36 Length.of.Defs: 0
% 0.13/0.36
% 0.13/0.36 Contains.Choice.Funs: false
% 0.19/0.37 (rf:0,axioms:11,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:13,loop_count:0,foatp_calls:0,translation:fof_full)...................................
% 8.97/9.26
% 8.97/9.26 ********************************
% 8.97/9.26 * All subproblems solved! *
% 8.97/9.26 ********************************
% 8.97/9.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:13,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:73,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:537,loop_count:0,foatp_calls:1,translation:fof_full)
% 9.15/9.39
% 9.15/9.39 %**** Beginning of derivation protocol ****
% 9.15/9.39 % SZS output start CNFRefutation
% See solution above
% 9.15/9.39
% 9.15/9.39 %**** End of derivation protocol ****
% 9.15/9.39 %**** no. of clauses in derivation: 538 ****
% 9.15/9.39 %**** clause counter: 537 ****
% 9.15/9.39
% 9.15/9.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:13,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:73,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:537,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------